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I know the answers to this question, but I\'m not sure how to work the problem.

ID: 1462446 • Letter: I

Question

I know the answers to this question, but I'm not sure how to work the problem. Thanks in advance!

A 1600 kg car travelling eastward at 32 m/s collides at an intersection with a 700 kg motorcycletravelling northward at 45 m/s. The two vehicles become entangled after the collision.  

a.) What is the magnitude and direction of the vehicle's velocity after the collision?

Answer: 26.1 m/s

b.) What is the direction of the car's velocity after the collision? (Measured from the east direction)

Answer: 31.6°

c.) How much kinetic energy is lost by the two vehicles during the collision?

Answer: -750,000 J

Explanation / Answer

Here ,

let the east be positive x - direction

north be the positive y - direction

Now, let the final speed is v

initial speed of motorcycle , u1 = 45 j m/s

initial speed of car , u2 = 32 i m/s

a) using conservation of momentum

v * (1600 + 700) = 45 * 700 j + 32 * 1600 i

solving for v

v = 22.3 i + 13.7 j m/s

v = sqrt(22.3^2 + 13.7^2) at arctan(13.7/22.3) degree

v = 26.2 m/s at 31.6 degree

the magnitude of final velocity is 26.2 m/s

b)

the direction of the car's velocity after the collision is 31.6 degree

b)

kinetic energy lost = initial kientic energy - final kinetic energy

kinetic energy lost = 0.5 * 1600 * 32^2 + 0.5 * 700 * 45^2 - 0.5 * (1600 + 700) * 26.2^2

kinetic energy lost = 738 544 J

the kinetic energy lost is 738 544 J