Two cars collide at an intersection. Car A , with a mass of 2000 kg , is going f

Question

Two cars collide at an intersection. Car A, with a mass of 2000 kg , is going from west to east, while car B, of mass 1500 kg , is going from north to south at 14.0 m/s . As a result of this collision, the two cars become enmeshed and move as one afterwards. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of 65.0 south of east from the point of impact.

How fast were the enmeshed cars moving just after the collision? (M/S)

How fast was car A going just before the collision? (M/S)

Explanation / Answer

here,

takin the direction towards east be + x axis and towards north be + y axis

speed of car b , ub = - 14 m/s j

ma = 2000 kg

mb = 1500 kg

let the speed of car A before collison be ua

and speed of emassed car be v

theta = 65 degree

using conservation of momentum along y axis

mb*ub = ( ma + mb) * v*sin(theta)

1500 * 14 = ( 3500) * v*sin(65)

v = 6.62 m/s

using conservation of momentum along x axis

ma*ua = ( ma+ mb) * v*cos(theta)

2000 *ua = ( 3500) * 6.62*cos(65)

ua = 4.9 m/s

the enmeshed cars moving just after the collision at the speed of 6.62 m/s

the speed of car A going just before the collision is 4.9 m/s

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