Question

A police jeep is chasing with, velocity of $45km/h$, a thief in another jeep moving with velocity $153km/h$. Police fires a bullet with muzzle velocity of $180m/s$. The velocity it will strike the car of the thief is

• A. $250m/s$
• B. $150m/s$
• C. $27m/s$
• D. $450m/s$

Answer 1

The correct option is B $150m/s$

Given:
Velocity of police jeep
$\left(V_P\right)=45km/h=45\times \frac{5}{18}=\frac{225}{18}=12.5m/s$
Velocity of thief jeep $\left(V_T\right)=153km/h=153\times \frac{5}{18}=42.5m/s$
Muzzle velocity of bullet
$\left(V_b\right)=180m/s$
Therefore, Effective speed of the bullet
= speed of bullet + speed of polic jeep
Effective speed of the bullet$=180m/s+12.5m/s$
Effective speed of the bullet $=192.5m/s$
Hence,
Velocity of the bullet with respect to thief’s car $\left(V_{BT}\right)$
$V_{BT}=\text{Effective speed of the bullet}-V_T=192.5m/s–42.5m/s{V}_{BT}=150m/s$