Question

A police jeep is chasing with velocity 45km/hr,a thief in another jeep moving with velocity 153km/hr.police fires a bullet with muzzel velocity of 180m/s.what is the velocity with which it will strike the car of the thief?

Answer 1

Answer on Question #44305 – Physics - Mechanics | Kinematics | Dynamics

A police jeep is chasing with velocity $45\mathrm{km/hr}$, a thief in another jeep moving with velocity $153\mathrm{km/hr}$. Police fires a bullet with muzzel velocity of $180\mathrm{m/s}$. What is the velocity with which it will strike the car of the thief?

Solution:

$$V_{P} = 45 \frac{\mathrm{km}}{\mathrm{hr}} = 12.5 \frac{\mathrm{m}}{\mathrm{s}} - \text{velocity of the police jeep};$$ $$V_{T} = 153 \frac{\mathrm{km}}{\mathrm{hr}} = 42.5 \frac{\mathrm{m}}{\mathrm{s}} - \text{velocity of the thief's jeep};$$ $$V_{B} = 180 \frac{\mathrm{m}}{\mathrm{s}} - \text{velocity of the bullet};$$

Now, since bullet is fired from police jeep which is going at $V_{P}$ therefore, velocity of bullet is

$$U = V_{B} + V_{P} = 180 \frac{\mathrm{m}}{\mathrm{s}} + 12.5 \frac{\mathrm{m}}{\mathrm{s}} = 192.5 \frac{\mathrm{m}}{\mathrm{s}}$$

To calculate velocity with which bullet will hit the thief we use concept of relative velocity.

Therefore, we have (Here $V_{B}$ is velocity of bullet and $V_{T}$ is velocity of thief)

$$V_{BT} = V_{B} - V_{T}$$ $$V_{BT} = 192.5 \frac{\mathrm{m}}{\mathrm{s}} - 42.5 \frac{\mathrm{m}}{\mathrm{s}} = 150 \frac{\mathrm{m}}{\mathrm{s}}$$

Answer: the velocity with which bullet will strike the car of the thief is equal to $150\frac{\mathrm{m}}{\mathrm{s}}$.

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