Question

During the filming of a certain movie scene, the director wants a small car (whose mass is m1) traveling due east at speed v1 to collide with a small truck (whose mass is m2) traveling north. The director also wants the collision to be arranged so that just afterward, the interlocked vehicles travel straight toward the camera. If the line between the camera and collision makes an angle of θ with respect to east, at what speed v2 should the trucker drive?

Answer 1

In this situation, we can use the principles of conservation of momentum to solve the problem. Before the collision, the momentum of the car traveling east is given by p1 = m1v1, where m1 is the mass of the car and v1 is its velocity. After the collision, the combined wreckage will travel straight towards the camera. Let's call the velocity of the combined wreckage v3. The angle between the line connecting the camera and the collision and the east direction is θ.

Step-by-step explanation:

In this situation, we can use the principles of conservation of momentum to solve the problem. Before the collision, the momentum of the car traveling east is given by p1 = m1v1, where m1 is the mass of the car and v1 is its velocity. The momentum of the truck traveling north is given by p2 = m2v2, where m2 is the mass of the truck and v2 is its velocity. The total momentum before the collision is the vector sum of p1 and p2. After the collision, the combined wreckage will travel straight towards the camera. Let's call the velocity of the combined wreckage v3. The angle between the line connecting the camera and the collision and the east direction is θ. Using vector addition, we can find the magnitude of v3 by taking the square root of the sum of the squares of v1 and v2: v3^2 = v1^2 + v2^2. Finally, we can find v3 by taking the square root of v3^2 and considering its direction based on θ.