A car with a mass of 980 kg is initially traveling east toward an intersection with a speed of vc=22.3m/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 45.0 degrees above the x-axis. Determine the initial speed of the truck (in a/s)

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MathPhys MathPhys · Answer 1 · 2019-11-05T21:41:43+01:00

Answer:

14.6 m/s

Explanation:

Momentum is conserved in the north:

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

After the collision, they stick together, so v₁ = v₂ = v.

m₁ u₁ + m₂ u₂ = (m₁ + m₂) v₂

(980 kg) (0 m/s) + (1500 kg) u = (980 kg + 1500 kg) vᵧ

1500 u = 2480 vᵧ

Momentum is conserved in the east:

m₁ u₁ + m₂ u₂ = (m₁ + m₂) v₂

(980 kg) (22.3 m/s) + (1500 kg) (0 m/s) = (980 kg + 1500 kg) vₓ

21854 = 2480 vₓ

vₓ = 8.81 m/s

The angle of v is 45.0°, so vᵧ = vₓ.

1500 u = 2480 (8.81 m/s)

u = 14.6 m/s