A motorcycle rider (68 kg) is moving at a constant speed of 144 km/hr down a str

Question

A motorcycle rider (68 kg) is moving at a constant speed of 144 km/hr down a straight road on his motorcycle (745 kg), when he encounters a bus moving in the opposite direction. The bus and passengers have a mass of 12580 kg. The bus is moving with constant speed of 62 km/hr. The bus driver is texting while driving. He crosses into oncoming traffic until the motorcycle collides head-on with the bus. Assume The collision lasts for 2/3 of a second and that the rider remains on the motorcycle during the collision.

a.) What is the force (magnitude and direction) experienced by the motorcycle rider during a perfectly inelastic collision?

b.) How many times his true weight is this?

c.) What is the velocity of the bus immediately after collision?

Explanation / Answer

Velocity after collision be v

m1*v1 + m2*v2 = (m1+m2)*v

(68+745) * (- 144*1000/3600) + (12580) * (62*1000/3600) = (68+745+12580) * v

v = 13.74 m/s

a) Force = Change in momentum/ time = 68*( 13.74 - (-40))/ (2/3) = 5454.2 N

Direction of force is opposite to the initial motion of rider

b) 5454.2/ 68*9.81 = 8.17 times the true weight of rider.

c) Velocity of the bus immediately after collison = 13.74 m/s = 49.46 km/hr

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