To determine the velocity with which the bullet will strike the thief's car, we first need to understand the scenario in terms of relative velocities.
- The police jeep is moving at a velocity of \(45 \, \text{km/h}\), which can be converted to meters per second for consistency in units:
- Since \(1 \, \text{km/h} = \frac{5}{18} \, \text{m/s}\), the conversion is:
- \(45 \, \text{km/h} = 45 \times \frac{5}{18} = 12.5 \, \text{m/s}\)
- The thief's jeep is moving at a velocity of \(153 \, \text{km/h}\):
- \(153 \, \text{km/h} = 153 \times \frac{5}{18} = 42.5 \, \text{m/s}\)
- The bullet is fired with a muzzle velocity of \(180 \, \text{m/s}\) relative to the police jeep. To find the velocity of the bullet with respect to the ground:
- Use the equation for relative velocity: \(V_{\text{bullet}} = V_{\text{muzzle}} + V_{\text{police}}\)
- \(V_{\text{bullet \, (ground)}} = 180 + 12.5 = 192.5 \, \text{m/s}\)
- Now, to find the velocity with which the bullet strikes the thief's car, we need the relative velocity of the bullet with respect to the thief's car:
- \(V_{\text{relative}} = V_{\text{bullet (ground)}} - V_{\text{thief}} = 192.5 - 42.5 = 150 \, \text{m/s}\)
Thus, the velocity with which the bullet will strike the car of the thief is 150 m/s.