Answer:
The speed of the vehicle is 156 miles per hour.
Explanation:
Let suppose that the Maglev, that is, a vehicle who works on the principle of superconductive magnetic levitation, moves at constant speed. Hence, the speed of the vehicle ([tex]v[/tex]), in miles per hour, is defined by this kinematic model:
[tex]v = \frac{s}{t}[/tex] (1)
Where:
[tex]s[/tex] - Travelled distance, in miles.
[tex]t[/tex] - Time, in hours.
If we know that [tex]s = 624\,mi[/tex] and [tex]t = 4\,h[/tex], then the speed of the vehicle is:
[tex]v = \frac{624\,mi}{4\,h}[/tex]
[tex]v = 156\,\frac{mi}{h}[/tex]
The speed of the vehicle is 156 miles per hour.
An athlete training for an event does 6.53 104 J of work during a workout and gives off 5.97 105 J of heat. Consider the athlete to be like a heat engine. (a) Determine the magnitude of the change in internal energy of the athlete. J (b) What is the efficiency of the athlete
Answer:
(a) The magnitude of the change in internal energy is 6.623 x 10⁵ J
(b) the efficiency of the athlete is 10.94 %
Explanation:
Given;
work done by the athlete (system), W = 6.53 x 10⁴ J
the heat given off by the athlete (system), Q = 5.97 x 10⁵ J
The simple diagram below will be used to illustrate the direction of the energy flow assuming a heat engine.
Q← ⊕ →W
The work, W, points away from the system since the system does the work
The heat, Q, points away from the system since heat is given off
Apply first law of thermodynamic;
ΔU = Q + W
where;
q is the heat flowing into or out of the system
(+q if the heat is flowing into the system
(-q if the heat is leaving the system
w is the work done by or on the system
(+w if the work is done on the system by the surrounding
(-w if the work is done by the system to the surrounding
Thus, from the above explanation, the change in internal energy of the system is calculated as;
ΔU = -Q - W
ΔU = - 5.97 x 10⁵ J - 6.53 x 10⁴ J
ΔU = -6.623 x 10⁵ J
The magnitude of the change in internal energy = 6.623 x 10⁵ J
(b) the efficiency of the athlete;
[tex]Efficiency = \frac{W}{Q} \times 100\%\\\\Efficiency = \frac{6.53 \times 10^4}{5.97 \times 10^5} \times 100\%\\\\Efficiency = 10.94 \ \%[/tex]
A voltage of 75 V is placed across a 150 Ω resistor. What is the current through the resistor?
Answer:
0.5 A
Explanation:
Applying,
V = IR.................. Equation 1
Where V = Voltage, I = current, R = Resistance.
make I the subject of the equation
I = V/R............... Equation 2
From the question,
Given: V = 75 V, R = 150 Ω
Substitute these values into equation 2
I = 75/150
I = 0.5 A.
Hence the cuurent through the resistor is 0.5 A
One solenoid is centered inside another. The outer one has a length of 50.0 cm and contains 6750 coils, while the coaxial inner solenoid is 3.0 cm long and 0.120 cm in diameter and contains 15 coils. The current in the outer solenoid is changing at 49.2 A>s. (a) What is the mutual inductance of these solenoids
Answer: The mutual inductance of these solenoids is [tex]2.88 \times 10^{-7} H[/tex].
Explanation:
Given: Length = 50.0 cm (1 cm = 0.01 m) = 0.50 m
[tex]N_{1}[/tex] = 6750
[tex]N_{2}[/tex] = 15
Radius = [tex]\frac{0.120 cm}{2} = 0.6 cm = 6 \times 10^{-4} m[/tex]
As inner of a solenoid resembles the shape of a circle. So, its area is calculated as follows.
[tex]Area = \pi \times r^{2} = \pi \times (6 \times 10^{-4})^{2}[/tex]
Formula used to calculate mutual conductance of two solenoids is as follows.
[tex]M = \frac{\mu_{o} \times A \times N_{1} \times N_{2}}{l}[/tex]
where,
M = mutual conductance
A = area
[tex]\mu_{o}[/tex] = relative permeability = [tex]4 \pi \times 10^{-7} Tm/A[/tex]
[tex]N_{1}[/tex] = no. of coils in outer solenoid
[tex]N_{2}[/tex] = no. of coils in inner solenoid
l = length
Substitute the values into above formula as follows.
[tex]M = \frac{\mu_{o} \times A \times N_{1} \times N_{2}}{l}\\= \frac{4 \pi \times 10^{-7} Tm/A \times \pi (6 \times 10^{-4})^{2} \times 6750 \times 15}{0.5 m}\\= 2.88 \times 10^{-7} H[/tex]
Thus, we can conclude that the mutual inductance of these solenoids is [tex]2.88 \times 10^{-7} H[/tex].
Dr. John Paul Stapp was a U.S. Air Force officer who studied the effects of extreme deceleration on the human body. On December 10, 1954, Stapp rode a rocket sled, accelerating from rest to a top speed of 282 m/s (1015 km/h) in 5.00 s, and was brought jarringly back to rest in only 1.40 s. Calculate his:
a. acceleration in his direction of motion
b. acceleration opposite to his direction of motion.
Answer: [tex]56.4\ m/s^2, 201.42\ m/s^2[/tex]
Explanation:
Given
Rocket attain a velocity of [tex]v=282\ m/s[/tex] in a time period of [tex]t=5\ s[/tex]
It was brought jarringly back to rest in only [tex]t'=1.4\ s[/tex]
Acceleration is the change in velocity of the object over a period of time
(a) Acceleration in his direction of motion
[tex]\Rightarrow a=\dfrac{v-0}{t}\\\\\Rightarrow a=\dfrac{282}{5}\\\\\Rightarrow a=56.4\ m/s^2[/tex]
(b) acceleration opposite to his direction of motion i.e. deceleration is
[tex]\Rightarrow a_d=\dfrac{0-v}{t'}\\\\\Rightarrow a_d=\dfrac{-282}{1.4}\\\\\Rightarrow a_d=-201.42 \ m/s^2\\\Rightarrow a_d=201.42\ \text{decelration}[/tex]
Matter's resistance to a change in motion is called _____ and is directly proportional to the mass of an object. For an object to change its state of motion, a force must be applied to it.
A. Velocity
B. Inertia
C. Distance
D. Area
Answer:
B) Inertia is the resistance of any physical object
How much time does it take for an eagle flying at a speed of 50 kilometers per hour to travel a distance of 2000 kilometers?
Answer:40 hour
Explanation:
Given this relationship, if you and your twin sibling (assuming you have the same mass) were to be separated by three times your original distance, what is the new gravitational force between you?
Answer:
The new force becomes (1/9)th of the original force.
Explanation:
The gravitational force between two masses is given by :
[tex]F=G\dfrac{m_1m_2}{r^2}[/tex]
Where
r is the distance between masses,
If the new distance is, r' = 3r
The new force is given by :
[tex]F'=G\dfrac{m_1m_2}{r'^2}\\\\F'=G\dfrac{m_1m_2}{(3r)^2}\\\\F'=\dfrac{1}{9}\times G\dfrac{m_1m_2}{r^2}\\\\F'=\dfrac{F}{9}[/tex]
So, the new force becomes (1/9)th of the original force.
HELPPP!!!! My teacher just asked why is water wet?
Can someone help me? I'll give brainliest
A metallic circular plate with radius r is fixed to a tabletop. An identical circular plate supported from above by a cable is fixed in place a distance d above the first plate. Assume that d is much smaller than r. The two plates are attached by wires to a battery that supplies voltage V.
Required:
a. What is the tension in the cable?
b. Compute the energy stored in the electric field after the top plate was raised.
Answer:
A) F = V²E_o•πr²/2d²
B) U = E_o•Aπr²V²/2d
Explanation:
A) Since we have two circular plates, the formula for the electric field is expressed as;
E = V/d
Where;
V is voltage
d is distance
However, the net electric field produced is given by;
E' = V/2d
The tension in the cable can then be expressed as;
F = qE'
Where q is charge
Thus;
F = qV/2d - - - (eq 1)
We also know that;
C = q/V = E_o•A/d
A is area = πr²
Thus;
q/V = E_o•πr²/d
q = VE_o•πr²/d
Let's put VE_o•πr²/d for q in eq 1 to get;
F = V²E_o•πr²/2d²
B) formula for the energy stored in the electric field is;
U = ½CV²
From earlier, we saw that; C = E_o•A/d
Thus;
U = ½E_o•AV²/d
A = πr²
Thus;
U = E_o•Aπr²V²/2d
a. Calculate the focal length of the mirror formed by the shiny bottom of a spoon that has a 2.51 cm radius of curvature.
Answer:
f = 1.255 cm
Explanation:
The Radius of Curvature:
The radius of that hollow sphere, whose part is the spherical mirror, is known as ‘The Radius of Curvature’ of mirror.
Focal Length:
The distance between principal focus and pole is called ‘Focal Length’. It is denoted by ‘F’
The focal length is basically equal to the half of the radius of curvature of the mirror:
[tex]f = \frac{r}{2}[/tex]
where,
f = focal length = ?
r = radius of curvature = 2.51 cm
[tex]f = \frac{2.51\ cm}{2}[/tex]
f = 1.255 cm
A 3.50 kg basket of cookies sits on a 2.00 m high shelf. What is the gravitational potential energy of the basket?
pls help
Answer:
68.6 J
Explanation:
Applying,
P.E = mgh............... Equation 1
Where P.E = Potential Energy of the basket, m = mass of the basket, g = acceleration due to gravity of the basket, h = height of the basket
From the question,
Given: m = 3.5 kg, h = 2.00 m
Constant: g = 9.8 m/s²
Substitute these values into equation 1
P.E = 3.5×2×9.8
P.E = 68.6 J
Hence the potential energy of the basket is 68.6 J
The quantum mechanical model of the hydrogen atom requires that if the orbital quantum number of the hydrogen atom is 4, there will be how many permitted orbital magnetic quantum numbers will be:_______
Answer:
-4, -3, -2, -1, 0, 1, 2, 3, 4
Explanation:
There are four sets of quantum numbers;
1) principal quantum number (n)
2)orbital quantum number (l)
3) magnetic quantum number (ml)
4) Spin quantum number (s)
These quantum numbers describes the probability of finding the electron within the atom.
The values of the magnetic quantum number depends on the orbital quantum number. The range of values of the magnetic quantum number is -l to +l
Hence, if the orbital quantum number of the hydrogen atom is 4, the permitted orbital magnetic quantum numbers will be; -4, -3, -2, -1, 0, 1, 2, 3, 4.
A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains air with a volume of 0.175 m^3 at a pressure of 0.350 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.365 m^3.
Required:
If the temperature remains constant, what is the final value of the pressure?
Answer:
the value of the final pressure is 0.168 atm
Explanation:
Given the data in the question;
Let p₁ be initial pressure, v₁ be initial volume.
After expansion, p₂ is final pressure and v₂ is final volume.
So using the following equations;
p₁v₁ = nRT
p₂v₂ = nRT
hence, p₁v₁ = p₂v₂
we find p₂
p₂ = p₁v₁ / v₂
given that; initial volume v₁ = 0.175 m³, Initial pressure p₁ = 0.350 atm,
final volume v₂ = 0.365 m³
we substitute
p₂ = ( 0.350 atm × 0.175 m³ ) / 0.365 m³
p₂ = 0.06125 atm-m³ / 0.365 m³
p₂ = 0.168 atm
Therefore, the value of the final pressure is 0.168 atm
I need an answer ASAP this is Mass Times acceleration
Answer:
[tex]force = mass \times acceleration \\ 1200 = 400 \times a \\ a = \frac{1200}{400} \\ a = 3 \: {ms}^{ - 2} [/tex]
Besides toxic pollution, the other types of pollution are sediment pollution, nutrient pollution, and bacterial pollution.
a. True
b. False
Answer:
a. True
Explanation:
Pollution can be defined as the physical degradation or contamination of the environment through an emission of harmful, poisonous and toxic chemical substances.
Aside from toxic pollution, the other types of pollution includes the following;
I. Sediment pollution.
II. Nutrient pollution.
III. Bacterial pollution.
Furthermore, particulate pollution is a form of pollution that is responsible for the degradation of the environment.
Particulate matter is also referred to as particle pollution or atmospheric aerosol particles and it can be defined as a complex microscopic mixture of liquid droplets and solid particles that are suspended in air. Other forms of particle pollution includes space debris and marine debris.
Some examples of particulate pollution are dusts, soot, dirt, smoke, etc.
Answer:a
Explanation:
If by some miracle you were able to run electrical appliances with the energy you obtained from food (maybe something like running on a human hamster wheel) how many pieces of pizza (at 300 Calories each) would you have to eat to watch the Super Bowl (4 hours long) on your HDTV (175 Watts)? Assuming an efficiency of 20% for the human body, your electrical energy output is only 20% of your caloric energy intake.
Answer:
1.00 × 10⁴ pieces of pizza
Explanation:
Step 1: Calculate the energy needed to watch the Super Bowl.
We need to produce energy to make an HDTV work (175 W) for 4 hours. First, we will convert, 4 hours to seconds using the conversion factor 1 h = 3600 s.
4 h × 3600 s/1 h = 14400 s
The energy required is:
14400 s × 175 J/s = 2.52 × 10⁶ J
We can convert this to calories using the conversion factor 1 cal = 4.184 J.
2.52 × 10⁶ J × 1 cal/4.184 J = 6.02 × 10⁵ cal
Step 2: Calculate the calories that the person should consume
Assuming an efficiency of 20% for the human body, the calories that a person should consume are:
6.02 × 10⁵ cal × 100/20 = 3.01 × 10⁶ cal
Step 3: Calculate the number of pieces of pizza to be consumed
Each piece of pizza contains 300 cal.
3.01 × 10⁶ cal × 1 piece/300 cal = 1.00 × 10⁴ pieces
Andrea, a 61.5 kg sprinter, starts a race with an acceleration of 3.700 m/s2. If she accelerates at that rate for 12.00 m and then maintains that velocity for the remainder of a 100.00 m dash, what will her time (in s) be for the race
Answer:
The total time it will take her to complete the race is 13.17 s
Explanation:
Given;
mass of the sprinter, m = 61.5 kg
acceleration of the sprinter, a = 3.7 m/s²
first distance covered, d₁ = 12 m
Determine her velocity for the first 12 m;
v² = u² + 2as
v² = 0 + (2 x 3.7 x 12)
v² = 88.8
v = √88.8
v = 9.42 m/s
Determine her time for the first 12 m;
v = u + at
9.42 = 0 + 3.7t₁
9.42 = 3.7t₁
t₁ = 9.42 / 3.7
t₁ = 2.55 s
Determine the time it will take her to complete the last 100 m at a constant velocity of 9.42 m/s
s = vt₂ + ¹/₂at₂²
s = vt₂ + ¹/₂(0)t₂²
s = vt₂
100 = 9.42t₂
t₂ = 100 / 9.42
t₂ = 10.62 s
The total time it will take her to complete the race = 2.55 s + 10.62 s
= 13.17 s
Probability of a woman wearing green to walk into a restaurant
A 615 N student standing on a scale in an elevator notices that the scale reads 645 N. From this information, the student knows that the elevator must be moving Group of answer choices You cannot tell if it is moving upward or downward. upward. downward.
Answer:
The elevator must be moving upward.
Explanation:
During the motion of an elevator, the weight of the person deviates from his or her actual weight. This temporary weight during the motion is referred to as "Apparent Weight". So, when the elevator is moving downward, the apparent weight of the person becomes less than his or her actual weight.
On the other hand, for the upward motion of the elevator, the apparent weight of the person becomes more than the actual weight of that person.
Since the apparent weight (645 N) of the student, in this case, is greater than the actual weight (615 N) of the student.
Therefore, the elevator must be moving upward.
Suppose we have a spaceship about the size of a typical ocean cruise ship today, which means it has a mass of about 120 million kilograms, and we want to accelerate the ship to a speed of 12 % of the speed of light. Suppose you want to generate the energy to get it to cruising speed using matter-antimatter annihilation.
Part A. How much energy would be required? (Hint: You can find the answer simply by calculating the kinetic energy of the ship when it reaches its cruising speed; because 12 % of the speed of light is still small compared to the speed of light, you can use the formula that tell us that kinetic energy = 12mv2.) Express your answer using two significant figures.
Part B. How does your answer compare to total world energy use at present, which is about 5×1022 joules per year? How does your answer compare to total world energy use at present, which is about joules per year? EspaceshipEworldenergyuse∼1 EspaceshipEworldenergyuse∼105 EspaceshipEworldenergyuse∼1020
Part C. The typical cost of energy today is roughly 5¢ per 1 million joules. Using this price, how much would it cost to generate the energy needed by this spaceship? Express your answer using two significant figures.
Answer: A 7.8 ·10^22 J B 1.6 times C 3.9 ·10^15 $
Explanation: A : Speed of light c = 3.0·10^8 m/s, 0.12·c = 3.6·10^7 m/s
Mass is 120·10^6 kg . Change of kinetic energy
E = ½mv² = 0.5 · 120·10^6 kg · (3.6·10^7 m/s)² = 7.776·10^22 J
B exponent is same , 7.776 / 5 = 1,55 times of energy use of Earth in year.
C Energy is 7.776·10^22 J / 10^6 = 7.776·10^16 MJ
Price is 0.05 $ · 7.776·10^16 MJ = 3.888·10^15 $
A. The energy required to get to the cruising speed is 7.8×10²² J
B. The energy needed will be 1.56 times the total world energy
C. The cost price required to generate the energy needed by the spaceship is $ 3.9×10⁵
A. Determination of the energy
Mass (m) = 120×10⁶ Kg
Velocity of light = 3×10⁸ m/s
Velocity of spaceship = 0.12 × 3×10⁸ = 3.6×10⁷ m/s
Energy (E) =?E = ½mv²
E = ½ × 120×10⁶ × (3.6×10⁷)²
E = 7.8×10²² JThus, the energy needed is 7.8×10²² J
B. Comparing the energy needed to the total world energy.
Energy needed = 7.8×10²² J
World energy = 5×10²² J
Energy needed / World energy = 7.8×10²² / 5×10²²
Energy needed / World energy = 1.56
Cross multiply
Energy needed = 1.56 × World energyThus, the energy needed is 1.56 times the World energy
C. Determination of the cost required to generate the energy
1×10⁶ J = $ 0.05
Therefore,
7.8×10²² J = (7.8×10²² × 0.05) / 1×10⁶
7.8×10²² J = $ 3.9×10⁵
Therefore, the cost required to generate the energy is $ 3.9×10⁵
Learn more: https://brainly.com/question/10703928
WILL REWARD BRAINLIEST
A thermonuclear fusion reaction cannot be maintained in the oceans of Earth because
A)the deuterium in the ocean is not radioactive.
B)the density is not high enough.
C) there is insufficient deuterium in the ocean.
D)the temperature is not high enough.
Answer: D) the temperature is not high enough.
Explanation:
The nuclear fusion reactions involve the fusion of the nucleus of the heavy metals. This is done in a nuclear reactor and energy is produced in the heat energy along with radiations. This system requires heat energy for the accomplishment of the nuclear reactions. The temperature of the system cannot be maintained inside the ocean so nuclear fusion will not occur in the ocean.
A set of charged plates is separated by 8.08*1^-5 m. When 2.24*10^-9 C of charge is placed on the plates, it creates a potential difference of 855 V. What is the area of the plates
q=CV
q=(ϵ0×A)/(d)×(V)
(2.24×10^−9)=((8.08×10^−4)(8.85×10−12))/(d)× (855)
d=2.7294×10^-3
the jackrabbit's powerful legs help it run fast to escape from predators, this is an
example of *
•A behavioral adaptation
•Poor breeding
•physical adaptation
•functional adaptation
Answer:
Physical adaptation
Explanation:
This is because the powerful legs of jackrabbit is an example of physical or structural adaptations because they are the physical features or characteristics that help jackrabit to survive or adapt in its natural environment. It makes it to run away from predators that might want to affect them. The structural adaptions help the animal to move ,eats and so on.
define the term area
[tex]\huge{\textbf{\textsf{{\color{pink}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}[/tex]
In geometry, the area can be defined as the space occupied by a flat shape or the surface of an object. The area of a figure is the number of unit squares that cover the surface of a closed figure.
Thanks Hope it helpsIn a region of space there is a uniform magnetic field pointing in the positive z direction. In what direction should a negative charge move to experience a force in the positive x direction
Answer:
the speed in -y
Explanation:
For this exercise we must use the right hand rule. The motion of a positive charge is given by.
Thumb points in the direction of speed
fingers extended in the direction of the magnetic field, + z axis
the palm in the direction of the force, as the charge is negative in the opposite direction of the force, axis + x
therefore the thumb is in the direction - y
the speed in -y
what is a crystal as applied in physics
Answer:
The correct answer is - A matter that has an ordered arrangement of atoms, molecules, or ions.
Explanation:
In physics, a crystal is a type of solid matter in which a highly arranged molecule or atoms present to form a lattice that extended in all directions. It is a lightweight clear solid which is normally is colorless.
It can be cubic, hexagonal, triclinic, monoclinic, orthorhombic, tetragonal, and trigonal that are ordered arrangments. Its internal symmetry is visible to its surface.
How does quantum theory explain blackbody radiators? O A. As the radiator is heated, it can have only certain specific temperature values. B. Raising the temperature results in the radiator giving off photons of high-energy ultraviolet light. C. Raising the temperature of the radiator causes more photons of a few possible energies to be emitted. D. As heat is added, the radiator emits photons across a wide range of visible-light frequencies SU
Answer: B. Raising the temperature results in the radiator giving off photons of high-energy ultraviolet light
Explanation:
Quantum theory explains the nature of matter and its behavior on the atomic level. It should be noted that at higher temperature, radiation is emitted by the blackbody at higher intensity and frequency.
Raising the temperature results in the radiator giving off photons of high-energy ultraviolet light. It should also be noted that there isn't a limit to the temperature of the blackbody.
The correct option is B.
Answer:
Explanation:
The CORRECT answer is C. Raising the temperature of the radiator causes more photons of a few possible energies to be emitted.
Quantum theory suggests that photons can only exist in a few possible energy states.
Energy coming off a radiator is usually in the infra-red light; not ultraviolet. So B is not the right answer.
Walking at a brisk pace, you cover 10 m in 5.0 s . How many seconds will you need to cover 50 m ?
A train with mass 3.3 x 107 kg starts from rest and accelerates to a speed of 42
m/s. What is the initial kinetic energy of the train?
Answer:
kinetic energy of the train = 2,910.6 x 10⁷ joule
Explanation:
Given:
Mass of train = 3.3 x 10⁷ kg
Speed of train = 42 m/s
Find:
kinetic energy of the train
Computation:
kinetic energy = (1/2)(m)(v²)
kinetic energy of the train = (1/2)(3.3 x 10⁷)(42²)
kinetic energy of the train = (1/2)(3.3 x 10⁷)(1,764)
kinetic energy of the train = (3.3 x 10⁷)(882)
kinetic energy of the train = 2,910.6 x 10⁷ joule
Answer: The initial kinetic energy of the train is [tex]2910.6 \times 10^{7} J[/tex].
Explanation:
Given: Mass = [tex]3.3 \times 10^{7} kg[/tex]
Speed = 42 m/s
Kinetic energy is the energy acquired by an object due to its motion.
Formula to calculate kinetic energy is as follows.
[tex]K.E = \frac{1}{2}mv^{2}[/tex]
where,
m = mass of object
v = speed of object
Substitute the values into above formula as follows.
[tex]K.E = \frac{1}{2}mv^{2}\\= \frac{1}{2} \times 3.3 \times 10^{7} kg \times (42 m/s)^{2}\\= 2910.6 \times 10^{7} kg m^{2}/s^{2} (1 J = 1 kg m^{2}/s^{2})\\= 2910.6 \times 10^{7} J[/tex]
Thus, we can conclude that the initial kinetic energy of the train is [tex]2910.6 \times 10^{7} J[/tex].
A student standing on the ground throws a ball straight up. The ball leaves the student's hand with a speed of 19.0 m/s when the hand is 2.50 m above the ground.
Required:
How long is the ball in the air before it hits the ground?
Answer: 4 s
Explanation:
Given
The ball leaves the hand of student with a speed of [tex]u=19\ m/s[/tex]
When the hand is [tex]h=2.5\ m[/tex] above the ground
Using the equation of motion we can write
[tex]h=ut+\dfrac{1}{2}at^2[/tex]
Substitute the values
[tex]\Rightarrow 2.5=-19t+0.5\times 9.8t^2\\\Rightarrow 4.9t^2-19t-2.5=0\\\\\Rightarrow t=\dfrac{19\pm \sqrt{(-19)^2-4\times 4.9\times (-2.5)}}{2\times 19}\\\Rightarrow t=4.0049\quad [\text{Neglecting the negative value of }t][/tex]
Thus, the ball will take 4 s to hit the ground.