A 1000-kg car approaches an intersection traveling north at 20.0 m/s. A 1200-kg car approaches the same intersection traveling east at 22.0 m/s. The two cars collide at the intersection and lock together. Ignoring any external forces that act on the cars during the collision, what is the velocity of the cars immediately after the collision?

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Physics

4 September, 01:45

A 1000-kg car approaches an intersection traveling north at 20.0 m/s. A 1200-kg car approaches the same intersection traveling east at 22.0 m/s. The two cars collide at the intersection and lock together. Ignoring any external forces that act on the cars during the collision, what is the velocity of the cars immediately after the collision?

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Gemma Holland · Answer 1

This problem applies momentum balance over the cars collided

m1v1y + m2v2y = (m1 + m2) v'y

0 + (1500 kg) (25.0 m/s) = (2500 kg) v'y

v'y = 15.0 m/s

Find the vector sum of the velocities:

v^2 = v'x^2 + v'y^2 = (8.00 m/s) ^2 + (15.0 m/s) ^2

v = 17.0 m/s

find the angle: θ = tan^-1 (15.0 m/s / 8.00 m/s) = 61.9°

now, the momentum: p = mv = (2500 kg) (17.0 m/s)

p = 4.25 x 10^4 kg x m/s at 61.9° N of E