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