A 1,383 kg purple car is driving southbound on a road and collides with a 1,827 kg orange car, that was traveling 31.87 m/s eastbound. The two cars collide and stick, sliding 14.54 meters before coming to rest. What was the initial velocity of the two-car system just after the collision? Take the coefficient of friction to be 0.463, and the acceleration due to gravity to be 9.8 m/s2. Answer to two decimal places.

Explanation:

We shall apply work energy theorem to calculate the initial velocity just after the collision .

Their kinetic energy will be equal to work done by friction .

force of friction = μ mg , where μ is coefficient of friction , m is total mass and g is acceleration due to gravity

force = .463 x 3210 x 9.8

= 14565.05 N

work done = force x displacement

= 14565.05 x 14.54 = 211775.88 J

now applying work energy theorem

1/2 m v² = 211775.88 , m is composite mass , v is velocity just after the collision

.5 x 3210 x v² = 211775.88

v² = 131.94

v  11.48 m /s

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