The distance travelled by the race car that is slowed down with a constant acceleration of - 11 m / s² before it comes to a stop is 22 m
a = ( v - u ) / t
a = Acceleration
v = Final velocity
u = Initial velocity
t = Time
a = - 11 m / s²
v = 0
u = 22 m / s
t = ( v - u ) / a
t = ( 0 - 22 ) / - 11
t = 2 s
s = ut + 1 / 2 at²
s = ( 22 * 2 ) + ( 0.5 * - 11 * 2 * 2 )
s = 44 - 22
s = 22 m
Therefore, the car will travel 22 m before it stops
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A bicycle wheel (a hoop) of radius 0.6 m and mass 5 kg is rotating at 4.00
rev/sec. After 25 sec the wheel comes to a stop because of friction. What is the
angular acceleration of the wheel?
The angular acceleration of the wheel 0.16 rad/sec².
What is acceleration?The rate at which an item changes its velocity is known as acceleration, a vector quantity. If an object's velocity is changing, it is acceleration.
The net acceleration that objects get as a result of the combined action of gravity and centrifugal force is known as the Earth's gravity, or g. It is a vector quantity whose strength or magnitude is determined by the norm and whose direction correlates with a plumb bob.
Given in the question,
angular acceleration = 4/25
angular acceleration = 0.16 rad/sec²
The angular acceleration of the wheel 0.16 rad/sec².
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a hoop with radius r, mass m and moment of inertia mr^2 rolls along a surface without slipping, at a constant velocity v. What is the angular momentum of the hoop about its center of mass?
mvr³ is the angular momentum of the hoop about its center of mass
L=mvr=Iω
L= angular momentum
m= mass
v=velocity
r= radius
L=mvr
L=mr²×r×v
L=mvr³
A characteristic known as angular momentum describes the rotating inertia of an item or set of objects when they are moving along an axis that may or may not pass through them. The Earth possesses spin angular momentum from its daily rotation around its axis and orbital angular momentum from its yearly revolution around the Sun. Since angular momentum is a vector quantity, its full representation calls for the identification of both a magnitude and a direction. An object in orbit has an angular momentum that is proportional to its linear momentum times the perpendicular distance r from the center of rotation to a line drawn through the center of gravity of the object, or just mvr.
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What is the argument by analogy(regarding other minds) and what is an objection against it?
The argument by analogy (regarding other minds) and the objection against it is that:
Bertrand Russell's "Comparison of Other Minds" aims to demonstrate the existence of minds other than his own by introspection and analogy; he thinks that by doing so, you can observe other people's activities and confidently conclude that they share your thoughts. It is all the time possible to make conclusions this way.What supports Russell's claim that there are other minds?Russell thinks there are other minds due to the fact that he can see behaviors in others that are similar to his own without giving them any conscious thought. He contends that thoughts are the root of all behavior, but what happens when a thought results in a reaction that one forces upon oneself.
Therefore, the traditional philosophical defense of the existence of other minds is the argument from analogy, which, as persuasively put forth by John Stuart Mill, a 19th-century empiricist, claims that since one's body and outward behavior are observably similar to those of others, one is justified by analogy in thinking that others have feelings similar to one's own and are not just automatons with similar bodies and outward behaviors.
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An object slides down a very smooth ramp,
with negligible friction. It slides with constant
acceleration a under the action of two forces:
the supporting force n exerted by the ramp,
and the force mg due to gravity exerted by
the earth.
What can you say about how the magnitude
of n compares to the magnitude of m g?
1. n is greater than mg.
2. None of these
3. n is less than m g.
4. Their magnitudes are equal, as is almost
always true on the earth's surface.
N is less than mg hence, It slides with constant acceleration a under the action of two forces
The rate at which an item changes its velocity is known as acceleration, a vector variable. If an object's velocity is changing, it is accelerating. A moving object can occasionally alter its velocity by the same amount every second. a moving object that changes its speed by 10 m/s per second. Since the velocity is changing by a fixed amount every second, this is known as a constant acceleration.
It is important to distinguish between an item with a constant acceleration and one with a constant velocity. Be not deceived! An object is accelerating if its velocity is changing, whether by a fixed amount or a variable quantity. Additionally, a moving item with a constant speed is not accelerating.
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A point mass of 0.5 kg moving with a constant speed of 5m/s on an elliptical track experiecnces an outward force oof 10N when at either endpoint of the major axis and a a=similar force of 1.25N at each end of thr minor sxis.How long are the axes of the ellipse?
The length of the axes of the eclipse are 1.25cm and 10cm.
How are the length of the eclipse found?With the formula, F = (mv²)/r
where F = force
m = mass
v = velocity and
r = diameter/length
To find how long the axes of the eclipse are at an outward force of 10N and a similar force of 1.25N:
For F₁ = 10N
10 = (0.5 x 5²)/r
10 = 12.5/r, cross multiply
r = 12.5/10 = 1.25cm
For F₂ = 1.25N
1.25 = (0.5 x 5²)/r
1.25 = 12.5/r, cross multiply
r = 12.5/1.25 = 10cm
The lengths of the eclipse are found by dividing the product of the mass and velocity by the first and second forces to get 1.25cm and 10cm
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When Galileo Galilei was alive, most scientists believed that heavy objects fall to Earth faster than light objects. Galileo conducted an experiment and found that objects of the same size and shape fall to Earth at the same speed, no matter their mass. What did Galileo most likely have to do in order to convince other scientists that his observations were correct?
A.
Keep the results to himself and wait for other scientists to conduct similar experiments.
B.
Conduct an experiment in which he tries to force one object to fall faster than a lighter object.
C.
Repeat the experiment multiple times in front of witnesses.
D.
Publish the results of the experiment.
Answer:
b. Is the answer because It depends on what Galileo Galilea thinks :,-)
Galileo most likely have to do this in order to convince other scientists that his observations were correct, is repeats the experiment multiple times in front of witnesses. So the correct option is C.
Galileo probably had to repeat his tests multiple times in front of witnesses to present convincing proof to other scientists rather than keeping the results to himself, making an object fall faster, or just publicizing his results.
Scientific certainty is produced by repeating an experiment and observing the outcomes, which is still regarded as a key component of the scientific method in modern times.
Galileo would have benefited from documenting his procedures and conclusions in a way that allowed other scientists to replicate his experiment and confirm his findings, even though it wasn't mentioned in your multiple-choice answers.
This concept is largely covered by the peer-review procedure used in contemporary science. So the correct option is C.
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You are gathering data about factor Y and factor X. A graph of your results in a straight line. What does this tell you about the relationship between y and x? What would the slope of this line represent? Explain your answers in terms of y and x
Explanation:
a straight line graph shows a linear relationship between and x and y, where if gradient is positive then it's a positive linear relationship (where when factor increases the other would also increase). if the the gradient is negative then it's a negative linear relationship where when factor decreases the other would also decrease.
the slope of the line is the gradient which can be determined using the equation,
gradient = y difference ÷ x difference
respective to which factor is presented by each axis.
hope it helps. :)
If you are given a measurement in scientific notation, how would you convert that into long form?
Two arrows are fired horizontally with the same speed of 30.0 m/s. Each arrow has a mass of 0.100 kg. One is fired due east and the other due south. Find the magnitude and direction of the total momentum of this two-arrow system. Specify the direction with respect to due east.
Why do we have to do square root of the Momentum, also at the last to find the direction why we do Tan^-1. Please explain.
Answer:
P = P1 + P2 where P is a vector quantity
P1 = P2 = .10 kg * 30.0 m/s = 3 kg-m/sec
P = (p1^2 + p2^2)^1/2 add vectors and find magnitude of resultant
p = (3.0^2 + 3.0^2)^1/2 = 4.24 length of resultant vector
Since vectors are at right angles p is the length of the hypotenuse
tan θ = 3.0 / 3.0 = 1 where theta is measured with respect to the positive x-axis and will be below that axis
θ = tan^-1 1 = 45 deg (45 degrees below positive x-axis)
One can find the value of tan θ from the length of the x-y vectors and from tan θ obtain θ
why does kinetic energy have two maxitans minimum values during each oscillation?
Answer:
it has water
Explanation:
water is good
An 75-kilogram skier slides on waxed skis along a horizontal surface of snow at constant velocity while pushing with his poles. What is the horizontal component of the force pushing him forward? (1) 0.05 N (2) 40 N (3) 37 N (4) 4 N
[Use: Ff = µ Fn; remember Fn = Fg = mg]
The horizontal component of the force pushing him forward is 37 N.
What is force?A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Frictional force due to ice, F = μN
Normal force N = mg = 75*9.8 = 735 N
Frictional force = 0.05*735 = 36.75 N
Coefficient of friction, μ for ice is 0.05
The horizontal component of the force pushing him forward is 37 N.
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A red 8-kg ball that is going 3-m/s collides with a 2-kg blue ball that is at rest. The blue
ball then goes 6-m/s. What is the red ball's speed?
Answer:
Explanation:
Given:
m₁ = 8 kg
V₁ = 3 m/s
m₂ = 2kg
V₂ = 0
V₂' = 6 m/s
__________
V₁' - ?
m₁V₁ + m₂V₂ = m₁V₁' + m₂V₂'
8·3 + 2·0 = 8·V₁' + 2·6
24 = 8·V₁' + 12
24 - 12 = 8·V₁'
12 = 8·V₁'
V₁' = 12 / 8 = 1.5 m/s
a nickel wire with a resistance of 25 Ω is connected across the terminals of a 3.0 v of a flashlight battery, how much current is in the wire?
The amount of current flowing in the wire, given that it has a resistance of 25 Ω and connected to a 3.0 V is 0.12 A
How do I determine the current in the wire?From Ohm's law, we understood that the voltage, current and resistance are related according to the following formula:
Voltage (V) = Current (I) × resistance (R)
V = IR
With the above formula, we can obtain the current in wire. Details below.
The following data were obtained from the question:
Resistance (R) = 25 ΩVoltage (V) = 3.0 VCurrent (I) =?Thus, the current can be obtained as follow:
Voltage (V) = Current (I) × resistance (R)
3 = Current × 25
Divide both sides by 25
Current = 3 / 25
Current = 0.12 A
Thus, we can conclude that the current in the wire is 0.12 A
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A coffeemaker has a resistance of 120 and draws a current of 10 A. What power does it use?
P = I²R = (10 A)² (120 Ω) = 120 000 Watts = 120 kW
a block of mass m=9.0kg and speed V and is behind a block of mass M=27 kg and speed of 0.50m/s, as shown in the figure. the surface is fricitonless, and the blocks suddenly collide and couple. after the collision, the blocks have a common speed of 0.90 m/s. how much kinetic energy of the blocks is lost due to the collision?
The kinetic energy of the blocks that is lost due to the collision is 8.64 J.
What is the initial speed of the smaller block?The initial speed of the smaller block is calculated by applying the following equation.
m₁u₁ + m₂u₂ = v(m₁ + m₂)
where;
m is the mass of the blocksu is the initial velocity of the blocksv is the common velocity of the blocks after the collision9u₁ + 27(0.5) = 0.9(9 + 27)
9u₁ + 13.5 = 32.4
9u₁ = 18.9
u₁ = 18.9/9
u₁ = 2.1 m/s
The total initial kinetic energy of the blocks is calculated as follows;
K.Ei = ¹/₂m₁u₁² + ¹/₂m₂u₂²
K.Ei = ¹/₂(9)(2.1)² + ¹/₂(27)(0.5)²
K.Ei = 23.22 J
The final kinetic energy of the blocks is calculated as follows;
K.Ef = ¹/₂(m₁ + m₂)v²
K.Ef = ¹/₂(9 + 27) x (0.9)²
K.Ef = 14.58 J
The change in the kinetic energy of the block is calculated as;
ΔK.E = K.Ef - K.Ei
ΔK.E = 14.58 J - 23.22 J
ΔK.E = -8.64 J
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is it true the greater the mass the greater the splash
Answer:If the momentum is large on the other hand, you will cause turbulences that make the water splash , So Yes
Explanation:
Using the page from the Chart of the Nuclides, select a nuclide that is radioactive and decays (changes) to another nuclide by emitting an Alpha particle. Is the new element radioactive and if it is, how do you know that? If the new nuclide is radioactive, what does it decay to?
Do the same thing with a nuclide that emits a Beta particle.
If a rock contains 75% lead 206 (Pb206) and 25% uranium 238 (U238), how old is the rock? Explain how you determined the answer.
Is it possible to have a rock of that age on Earth, and what is the reason for your answer?
The age of the rock is 9 * 10^9 years and there is no rock that can be as old as this age on earth.
What is radioactive decay?The term radioactive decay has to do with the process by which a radioactive nuclide disintegrates so as to obtain the daughter nucleus. The radioactive decay may occur by alpha or by beta radiation.
In this case, we are told that only 25% of the original uranium 238 isotope of half life 4.5 * 10^9 years still remains.
Using the formula;
0.693/[tex]t_{\frac{1}{2}[/tex] = 2.303/t log (No/N)
[tex]t_{\frac{1}{2}[/tex] = half life of the isotope
N= amount of isotope at time t
No = amount of isotope initially present
Then;
0.693/4.5 * 10^9 = 2.303/t log(No/0.25No)
1.54 * 10^-10 = 1.39/t
t = 1.39/1.54 * 10^-10
t = 9 * 10^9 years
There is no rock that is this much old since the average age of the earth is 4.5 billion years.
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A car of mass 1500kg travelling at a velocity of 10 m/s crashes into the back of a moving car of mass 1500kg travelling at a velocity of 5 m/s. The vehicles move together after the impact Calculate their velocity?
Answer:
M1 V1 + M2 V2 = (M1 + M2) V
Conservation of momentum where V is speed of combined vehicles
V = (1500 * 10 + 1500 * 5) / (1500 + 1500) = 7.5 m/s
Using the given data table, calculate the acceleration of the skateboarder. You can use either form of the
equation:
The acceleration of skateboard on road A will be 7.74 [tex]m/s^{2}[/tex]
The acceleration of skateboard on road B will be 3.87 [tex]m/s^{2}[/tex]
The acceleration of skateboard on road C will be 9.68 [tex]m/s^{2}[/tex]
force = mass * acceleration
mass1 = 62 kg
force1 = 480 N
acceleration1 = force / mass
= 480 / 62 = 7.74 [tex]m/s^{2}[/tex]
mass2 = 62 kg
force2 = 240 N
acceleration 2 = 240 / 62 = 3.87 [tex]m/s^{2}[/tex]
mass 3 = 62 kg
force 3 = 600 N
acceleration 3 = 600 / 62 = 9.68 [tex]m/s^{2}[/tex]
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A 9.25 kg bowling ball is hung on a 9.5 m long rope. It is then pulled back until the rope makes an angle of 35° with the vertical and released. Find the tension in the rope when the ball is at the lowest point. Give your answer in N and with 3 significant figures.
Answer:
123.6 N
Explanation:
I will try to answer this
Find height of the ball
9. 5 - 9.5 cos 35 = 1.72 m of potential energy
PE = mgh will be converted to KE at the bottom of the swing
mgh = 1/2 m v^2
sqrt( 2 gh ) = v at the bottom = 5.81 m/s
then the tension is the mass times the acceleration of gravity PLUS the acceleration of circular motion v^2 / r
F = ma
F = 9.25 kg ( 9.81 m/s^2 + 5.81^2 / 9.5 m/s^2 ) = tension = 123.6 N
(Let me know if this is incorrect, and I will research a bit more)
A space station in deep space is spun like a giant
wheel to produce centrifugal force so the occupants
experience artificial gravity of one g. How does a
clock at the rim of the space station compare with
one residing at the hub? What does this say about
the behavior of a clock sitting on the surface of a
planet with a surface gravity of one g?
The behavior of a clock sitting on the surface of a planet with a surface gravity of one g says that rim clock always runs slower
Gravity is the principal force acting on a body in projectile motion when it is hurled at a specific angle. The power with which the body is originally thrown determines maximum height and how far it will travel. When an object moves in a projectile motion, there are numerous instances in daily life. For instance, a basketball player will obliquely toss the ball at a specific angle towards the direction of the hoop. The ball then rises and descends like a missile in the direction of the basket. Other sports like cricket, football, and soccer may demonstrate this.
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kari ann is pulling a bookcase across her bedroom floor. what are three reasons that she might find it hard to accelerate the bookcase? (hint: link to both labs as well as newton's 1st law)
Three reasons why it may be difficult to accelerate the bookcase are;
1) Inertia that acts on the book case
2) Frictional force that prevents the book case from moving
3) The weight of the book case.
Why is there difficulty in moving the suitcase?We know that the Newton law states that a body would tend to remain at a state of rest or uniform motion unless it is acted upon by unbalanced forces. When the book lies without movement it is acted upon by its weight and the reaction which are exactly balanced. The inertia is the reluctance of the book to move.
As the book begins to move when pull, the friction that is acting on the pull would also militate against the forward motion of the book as it acts in the opposite direction.
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3. An object released from rest at time t = 0 slides down a frictionless incline a
distance of 1 m during the first second. The distance traveled by the object
during the time interval from t = 2 s to t = 3 s is:
(A) 1 m
(B) 2 m (C) 3 m
(D) 4 m (E) 5 m
The distance traveled by the object during the time interval from t = 2 s to t = 3s is 3m. Option C.
From the formula d = ½ at2 the displacement is proportional to the square of time. If you run twice as far from the rest, the displacement will quadruple (or 4m). Since the object has already moved 1 m in the first second, the remaining 3 m have moved in time intervals from 1 to 2 seconds.
This means that the velocity and net force in the direction normal to the plane must be zero. Assuming the plane is frictionless means that the plane exerts no force on the block parallel to the surface. For angular frictionless tilt, the acceleration is the result of the gravitational acceleration multiplied by the sine of the angle.
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Determine the distance that a car recovers after 5 seconds if it travels at a speed of 10m/s.
We first apply the data to the problem.
Data:
V = 10m/sT = 5sD = ?Then, we apply the formula that is.
Formula:
D = V • TFinally we develop the problem.
Developing:
D = (10m/s) • (5s)D = 50mThe car travels a distance of 50 meters.
Anatomy and physiology can be classified as ____ science
A. behavioral
B. life
C. physical
D. formal
B is your answer, hope it helps.
Pedro feels his best after chatting with a friend and discussing new ideas with his teammates. Which function do these preferred activities show? A. Thinking B. Introversion C. Knowing D. Extroversion
The fact that Pedro likes to talk to people means that Pedro is an extrovert.
Who is an extrovert?We define an extrovert as a person that is able to interact very much freely with other people. It is one of the kinds of temperaments that a person can have. We know that people that can have very different temperament types and these are the things that determine the behavior of a person.
Thus, a person acts in accordance with the kind of temperaments that a person has. Just as we can see in the person of Pedro. We are told in his case that the person Pedro would always like to talk with is friends and the team mates which suggests that he must like to associate with other people.
From our definition of the person of Pedro in the lines that are above, we can say the Pedro is an extrovert.
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Which process is likely to happen more quickly: the physical weathering of rock by plant roots or the physical weathering of rock by the repeated thawing of water? Explain your answer
The physical weathering of rock by the repeated thawing of water is likely to happen more quickly than the physical weathering of rock by plant roots.
How does repeated thawing of water causes the rock to weather?
First, the physical weathering of rock is usually caused by water (which can come from rain or erosion), ice, plant roots, and even animals. These agents ensure the rock is broken down into smaller particles or sizes.
So, the thawing of water ensures continuous freezing and melting of water which allows water in the form of ice to build up in the cracks of rocks after expanding on freezing. This makes the rock breaks apart due to the pressure that is built in the crack.
However, physical weathering from the root of plants is slower compared to that of the repeated thawing of water. Though both processes needed time, but it will take more time for the roots in a crack. For the plant roots to get cracks to grow into, it needs repeated thawing of water to create that crack or other agents of rock weathering to create the crack.
In summary, repeated thawing of water makes rocks more susceptible to chemical and biological weathering. The weathering of rock by plant roots will need the plant to grow and survive in the first place, which might take more time.
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A horizontal pipe 10.0 cm in diameter has a smooth reduction to a pipe 5.00 cm in diameter. If the pressure of the water in the larger pipe is 8.00 104 Pa and the pressure in the smaller pipe is 6.00 104 Pa, at what rate does water flow through the pipe?
The volume flow rate at which the water flows is 0.0188 m³/s
How to find what rate does water flow through the pipe?Since the horizontal pipe 10.0 cm in diameter has a smooth reduction to a pipe 5.00 cm in diameter and If the pressure of the water in the larger pipe is 8.00 × 10⁴ Pa and the pressure in the smaller pipe is 6.00 × 10⁴ Pa, since we require the rate at which water flows through the pipe, we use Bernoulli's equation at constant height to find the speed of flow.
What is Bernoulli's equation?Bernoulli's equation governs flows through pipes. It is given by
P₁ + ρgh₁ + 1/2ρv₁² = P₂ + ρgh₂ + 1/2ρv₂² where
P₁ = pressure at point 1, h₁ = height at point 1, v₁ = speed at point 1, P₂ = pressure at point 2, h₂ = height at point 2, and v₂ = speed at point 2With h₁ = h₂, the Bernoulli's equation becomes
P₁ + 1/2ρv₁² = P₂ + 1/2ρv₂²
Using the volume flow rate equation
Q = A₁v₁ = A₂v₂ where
A₁ = cross- sectional area at point 1 = πd₁²/4 where d₁ = diameter at point 1v₁ = speed at point 1, A₂ = cross- sectional area at point 2 and d₂ = diameter at point 1 = πd₂²/4v₂ = speed at point 2So, A₁v₁ = A₂v₂
(πd₁²/4)v₁ = (πd₂²/4)v₂
d₁²v₁ = d₂²v₂
Making v₂ subject of the formula, we have
v₂ = d₁²v₁/d₂²
v₂ = (d₁/d₂)²v₁
Substituting v₂ into the Bernoulli equation, we have
P₁ + 1/2ρv₁² = P₂ + 1/2ρv₂²
P₁ + 1/2ρv₁² = P₂ + 1/2ρ(d₁/d₂)⁴v₁²
Making v₁ subject of the formula, we have
1/2ρv₁² - 1/2ρ(d₁/d₂)⁴v₁² = P₂ - P₁
1/2ρ[1 - (d₁/d₂)⁴]v₁² = P₂ - P₁
v₁² = √{2(P₂ - P₁)/ρ[1 - (d₁/d₂)⁴]}
Given that
P₁ = pressure in larger pipe = 8.00 × 10⁴ Pa d₁ = diameter of larger pipe = 10.0 cmP₂ = pressure in smaller pipe = 6.00 × 10⁴ Pa d₂ = diameter of smaller pipe = 5.00 cmρ = density of water = 1000 kg/m³Substituting the values of the variables into the equation, we have
v₁ = √{2(P₂ - P₁)/ρ[1 - (d₁/d₂)⁴]}
v₁ = √{2(6.00 × 10⁴ Pa - 8.00 × 10⁴ Pa)/1000 kg/m³[1 - (10.0 cm/5.0 cm)⁴]}
v₁ = √{2(- 2.00 × 10⁴ Pa)/1000 kg/m³[1 - 2⁴]}
v₁ = √{(- 4.00 × 10⁴ Pa)/1000 kg/m³[1 - 8]}
v₁ = √{(- 4.00 × 10⁴ Pa)/1000 kg/m³[-7]}
v₁ = √{(40.0 × 10³ Pa)/7 × 10³ kg/m³}
v₁ = √{(40.0/7 Pam³/kg}
v₁ = √{5.7143 Pam³/kg}
v₁ = 2.39 m/s
Since the volume flow rate Q = A₁v₁ = (πd₁²/4)v₁
Given that
d₁ = diameter of larger pipe = 10.0 cm = 0.1 m and v₁ = speed in larger pipe = 2.39 m/sSubstituting the values of the variables into the equation, we have
Q = (πd₁²/4)v₁
Q = π(0.1 m)²/4 × 2.39 m/s
Q = π × 0.01 m²/4 × 2.39 m/s
Q = π × 0.0239 m³/s/4
Q = 0.0751 m³/s ÷ 4
Q = 0.0188 m³/s
So, the water flows at a rate of 0.0188 m³/s
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What work is done by a forklift raising a 583 kg box a distance of 1.2 m?
The work that is done by a forklift raising a 583 kg box a distance of 1.2m is 699.6N.
How to calculate work done?Work refers to the measure of energy expended in moving an object. It is most commonly calculated by multiplying the force by the distance.
This means that no work is done if the object does not move. This means that the work done can be calculated as follows:
Work done = Force × distance
According to this question, a forklift raises a 583kg box over a distance of 1.2m. The work done can be calculated as follows:
Work done = 583kg × 1.2m
Work done = 699.6N
Therefore, 699.6N is the force required to lift the box.
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You observe an X-ray source to vary on a timescale
of 0.001 seconds. What is the upper limit for the
size of the X-ray emitting region? What is the mass
of a black hole with a Schwarzschild radius of this
size?