A car moving east at 30m/s runs head-on into a 3000 kg truck moving west at 20m/s. The vehicles stick together. Use the concept of the centre of momentum frame to determine how much kinetic energy is lost.

Short Answer

Expert verified

The recoil speed of the Earth is2.3×10-24m/s.

Step by step solution

01

Given information

Mass of the ball ism=155g.

Initial speed of the ball is 44m/s.

Mass of the Earth is M=6×1024kg.

02

The concept of law of conservation of linear momentum

The law of conservation of linear momentum asserts that the vector sum of a system of two colliding objects is constant and unaffected by their mutual interaction when no external forces are acting on the system.

03

Derive formula for momentum

We can apply the law of conservation of linear momentum since there are no external forces on the system.

Pi=Pf

Break down the formula based on its mass and velocities.

mvi=2mv1,fv1,f=vi2mvi=2mv1,f

04

Calculation for velocity

Substitute the values to the derived formula.

vearth=2mvball,iM=2(0.155kg)(44m/s)6×1024kg=2.3×10-24m/s

Therefore, the recoil speed of the Earth is2.3×10-24m/s.

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