A 1000- kg car collides with a 1500- kg car that was initially at rest at the or

Question

A 1000- kg car collides with a 1500- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 15.0 km/h in a direction of 20 degree with respect to the positive x axis. The heavier car moves at 18 km/h at -42 degree with respect to the positive x axis. What was the initial speed of the lighter car (in km/h)? The car is not coming in along the x-axis in the picture. Calulate the x and y values of the initial monenta and compute the speed and direction of the velocity. What was the initial direction (as measured counterclockwise from the x-axis)?

Explanation / Answer

here,

m1 = 1000 kg

m2 = 1500 kg

v1 = 15 km/h

theta 1 = 20 degree

v2 = 18 km/h

theta2 = - 42 degree

let the angle of initial velocity v of lighter car be theta

using conservation of momentum along x axis

m1 * v*cos(theta) = m1 * v1 * cos(theta1) + m2 * v2 * cos( theta2)

1000 * v*cos(theta) = 1000 * 15 * cos(20) + 1500 * 18 * cos(42) ....(1)

using conservation of momentum along y axis

- m1 * v*sin(theta) = m1 * v1 * sin(theta1) + m2 * v2 * sin( theta2)

- 1000 * v*sin(theta) = 1000 * 15 * sin(20) - 1500 * 18 * sin(42)..(2)

solving equation (1) and (2)

v = 38.72 km/h

theta = 28.06 degree

the initial velocity of the car is v = 38.72 km/h and 151.94 degrees from the +x axis counterclockwise

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