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An armored vehicle of length 2 m and width 3 m moves along the x-axis at a speed of 20 m/s. A bullet, observed from the ground, travels in a direction making an angle arctan(1/2) with the x-axis. The bullet enters through one corner of the vehicle and exits through the diagonally opposite corner, with no interaction between bullet and vehicle. If the bullet takes t seconds to cross the vehicle, find the value of 20t.

1. 4
2. 3
3. 5
4. 2

Correct answer: 4

Solution

In the vehicle frame the bullet must cover 2 m longitudinally and 3 m laterally. The constraint 3*vx_car = 2*vy_car, combined with the ground-frame angle condition, gives bullet speed 15*sqrt(5) m/s, yielding t = 0.2 s and 20t = 4.

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