2d Momentum Problem 1: You are investigating the scene of an accident involving

Question

2d Momentum

Problem 1: You are investigating the scene of an accident involving a 2000 kg truck originally traveling
south and a 1200 kg car orignially traveling west. The two vehicles became attached when the collision
occured and came to rest 9.18 meters away from the point of collision at an angle of 51.34 degrees south
of west. The coecient of friction between the vehicles and the road is k = 0:8

Calculate the initial
speeds of the TRUCK and the CAR.

Explanation / Answer

here,

let the final speed of the combination be v

distance to rest , s = 9.18 m

a = u*g

a = 7.84 m/s^2

using third equation of motion

0 - v^2 = - 2 * 7.84 * 9.18

v = 12 m/s

theta = 51.34 degree

let their initial velocity be vc and vt

mass of truck , mt = 2000 kg

mass of car , mc = 1200 kg

using conservation of momentum in x direction

( mt + mc) * v*cos(theat) = mc*vc

( 2000 + 1200) * 12 * cos(51.34) = 1200 *vc

vc = 20 m/s

using conservation of momentum in y direction

( mt + mc) * v*sin(theat) = mt*vt

( 2000 + 1200) * 12 * sin(51.34) = 2000 *vt

vt = 15 m/s

the initial speed of truck is 15 m/s and the car is 20 m/s

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