Question

A blue car with mass mc = 427 kg is moving east with a speed of vc = 20 m/s and collides with a purple truck with mass mt = 1282 kg that is moving south with a speed of vt = 13 m/s . The two collide and lock together after the collision. Let us define to the east is the +x direction and to the north is the +y direction. What is the magnitude of the initial momentum of the car?

Answer 1

Answer:8540 kg-g/s

Step-by-step explanation:

Given

mass of blue car
`m_c=427 kg`

velocity of blue car
`v_c=20 m/s`

mass of the truck
`m_t=1282 kg`

speed of truck
`v_t=13 m/s`

After collision they stick and lock together

Let v be the velocity of combined system at angle \theta from vertical

Conserving momentum in east direction

`m_c* v_c=(m_c+m_t)v\cos \theta`

`427* 20 =1709* v\cos \theta`------1

Conserving Momentum in Y direction

`m_t* v_t=(m_c+m_t)v\sin \theta`

`1282* 13 =1709* v\sin \theta`-------2

squaring and then adding 1 & 2 we get

`(8540)^2+(16666)^2=(1709)^2\cdot v^2`

v=10.95 m/s

initial momentum of car
`=427* 20=8540 kg-m/s`