A car with a mass of 980 kg is initially traveling east toward an intersection w

Question

A car with a mass of 980 kg is initially traveling east toward an intersection with a speed of vc = 21.5 m/s and a 1500 kg pickup is traveling north toward the same intersection. The car and truck collide at the intersection and stick together. After the collision, the wreckage (car and truck) moves off in a direction of 43.0° above the x-axis. Determine the initial speed of the truck and the final speed of the wreckage.

Initial speed of the truck= ______m/s

Final speed of the wreckage: _______ m/s

Explanation / Answer

Conserve momentum: initial p = final p
initial p = 980kg * 21.5m/s i + 1500kg*u j = 21070kg·m/s i + 1500kg*u j
u = initial velocity of pickup
final p = (980kg + 1500kg) * v * (cos43º i + sin43º j) = 1814kg * v i + 1691kg * v j
v = final speed of wreckage

Separate the i's and j's into their own equations... because the x direction is independent of the y direction

Looking at the x-components, we have
21070kg·m/s = 1814kg * v v = 11.61 m/s final speed
Looking at the y-components, we have
1500kg * u = 1691kg * 11.61m/s u = 13.088 m/s initial speed of pickup

Always break vectors down into the perpendicular components.

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