Question

A police van moving on a highway with a speed
of 30 km h-' fires a bullet at a thief's car
speeding away in the same direction with a
speed of 192 km h-!. If the muzzle speed of the
bullet is 150 m sl, with what speed does the
bullet hit the thief's car ?
(a) 95 m s' (b) 105 m s'
(c) 115 m s (d) 125 m s!​

Answer 1

(C) 105 m s^-1

Given:

Speed of the police van vp

= 30 km h^-1

Converting into m/sec:

= 30 x 1000 / 3600

= 25/3 ms^-1

Speed of the thief's car vt

= 192 x 5/18 ms^-1

= 160/3 ms^-1

Formula we have to use here to calculate the speed of the bullet:

= Speed of police van + speed with which the bullet was actually fired

Calculating the Speed of the bullet by using the formula:

= 25/3 + 150

= 475 / 3 ms^-1

Calculating the relative velocity of thief's car with respect to bullet:

vbt = vb - vt

Substituting the values into this formula we get:

Vbt = (475/3 - 160/3)

Vbt = 315/3

Vbt = 105 ms^-1

Therefore the speed at which the bullet hits the thief's car is 105 ms^-1. Option (C) 105 m s^-1 is the correct answer.

Answer 2

Given,

➡️Speed of the

Van (Vp) = 30km h^-1 = 25/3ms^-1

➡️Speed of the thief

car (Vt) = 160/3ms^-1

To Find:-

Speed of the bullet

Relative velocity of the thief car

Calculations:-

--->Speed of the man + Speed of the bullet (fired)

------->25/3 +150

------->475/ms^-1

Relative velocity of the thief car:-

Vbt = vb - Vt

Vbt = (475/3)-(160/3)

Vbt = 315/3

Vbt = 105ms^-1

So,

Option.C is the correct answer

Explore More:-

Speed:- Speed is the distance traveled per unit of time. It is how fast an object is moving.

Speed = Distance/Time

• Speed is the scalar quantity that is the magnitude.

• Speed is a scalar quantity.

• SI unit of speed is m/s

Velocity:- velocity of an object can be defined as the rate of change of the object's position with respect to a frame of reference and time.

V = D/t

• Velocity is a vector quantity.

• SI unit of velocity is m/s

• velocity is the speed at which something moves in one direction