A gun kept on a straight horizontal road is used to hit a car travelling on the same road away from the gun at a uniform speed of 14.14 ms -1. The car is at a distance of 150 m from the gun when it is fired at an angle of 45° to the horizontal. What is the distance of the car from the gun when the shell hits it?

250 m

Explanation:

In projectile, range is given as;

R = (v²sin 2θ)/g

We are given θ = 45°

Thus range of shell is;

R = (v²sin (2 × 45))/g

R = v²/g

Now, distance for the shell to hit the car will be; 150 + 14.14t

This will be equal to the range of shell;

150 + 14.14t = v²/g

Where t is time of flight

Now, time of flight is given by;

t = (2vsin θ)/g

t = (2v sin 45)/g

In surf form, we have;

t = (2v/(g√2))

Simplifying further gives;

t = (v√2)/g

Plugging this value of t into the distance equation gives;

150 + 14.14(v√2)/g = v²/g

Assuming g is 10 m/s², we have;

150 + 14.14(v√2)/10 = v²/10

Multiply through by 10 to get;

1500 + 14.14(v√2) = v²

v² - 20v - 1500 = 0

From quadratic equation calculator, we have; v = 50 m/s

Thus, t = (50√2)/g

t = (50√2)/10

t = 5√2

Plugging this into the distance equation gives;

Distance = 150 + 14.14(5√2) = 250 m

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.