Question

As shown below, a 840 kg car traveling east collides with a 1730 kg pickup truck that is traveling north. The two vehicles stick together as a result of the collision. After the collision, the wreckage is sliding at v_f = 19 m/s in the direction θ = 25° east of north. Calculate the speed of each vehicle before the collision. The collision occurs during a heavy rainstorm so you can ignore friction forces between the vehicles and the wet road. Express your answers using apropriate mks units.

A.) v_car,i =

B.) v_truck,i =

C.) Determine what fraction of the total initial KE is turned into thermal energy as a result of the collision.

ΔTE

KEtotal,i

=

Answer 1

Let us assume x-axis and y-axis of Cartesian coord system coincide with East and North

directions as shown in figure.

momentum = mass x velocity

momentum before collision along x-axis :- 840 x uc

momentum after collision along x-axis :- ( 1730 + 840 ) x 19 cos25

by conservation of momentum :- 840 x uc = ( 1730 + 840 ) x 19 cos25

From above equation , we get , velocity of car , uc = 52.68 m/s

momentum before collision along y-axis :- 1730 x ut

momentum after collision along y-axis :- ( 1730 + 840 ) x 19 sin25

by conservation of momentum :- 1730 x ut = ( 1730 + 840 ) x 19 sin25

From above equation , we get , velocity of ut = 11.93 m/s

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Kinetic energy KEi before collision

Kinetic energy KEf after collision

Loss of kinetic energy = 8.251 x 105 J