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 $150~m/s,$ with what speed does the bullet hit the thief's car?

• A. $475/3$ m/s
• B. $160/3~m/s$
• C. $150~m/s$
• D. $105~m/s$

Hint:

Impact speed depends on the relative velocity of the objects.

Answer 1

The Correct Option is D

Step 1: Concept
Relative Velocity: $v_{relative} = v_{bullet} - v_{thief}$.
Step 2: Analysis
- Convert speeds to m/s: $v_{police} = 30 \times \frac{5}{18} = \frac{25}{3}$ m/s. - $v_{thief} = 192 \times \frac{5}{18} = \frac{160}{3}$ m/s. - Muzzle speed is relative to the van: $v_{bullet} = v_{muzzle} + v_{police}$. - $v_{bullet} = 150 + \frac{25}{3} = \frac{475}{3}$ m/s.
Step 3: Calculation
- Speed of impact = $v_{bullet} - v_{thief}$. - Impact speed = $\frac{475}{3} - \frac{160}{3} = \frac{315}{3} = 105$ m/s.
Step 4: Conclusion
Hence, the bullet hits at 105 m/s.
Final Answer:(D)