Question

Bill forgets to put his car in park and it starts rolling west. When it is moving at a speed of 3.5m/s, it collides with Tanya’s car, which is moving at a speed of 2m/s east. Bill’s car bounces backward (to the east) at a speed of 2m/s. Bill’s car has a mass of 900kg, and Tanya’s car has a mass of 1100kg. A. What is the velocity of Tanya’s car after the collision?B. Assuming all lost kinetic energy is converted to hear during the collision?

Answer 1

For A.

Bill's car

mass=900 kg

speed=3.5m/s towards west

Tanya's car

mass = 1100 kg

speed = 2 m/s towards East

The momentum

$P=P1-P2$

For P1 and P2

$P_1=900(3.5)=3150\text{ kg m/s}$$P_2=1100(2)=2200\operatorname{kg}\text{ m/s}$$P=3150-2200=950\text{ kgm/s}$

then for the velocity, we have the final momentum

We can calculte the final momentum of Bill's

$P=900(2)=1800\text{ kgm/s}$

$1100v-1800=950$

v is the velocity of Tanya’s car after the collision, so we need to isolate the v

$v=\frac{950+1800}{1100}=2.5\text{ m/s }$

The velocity of Tanya's car after the collision is 2.5 m/s towards west

For B.

First, we need to calculate the kinetic energy before the collision of Bill's car and Tanya's car

$KE_B=\frac{1}{2}m_Bv^2_B+=\frac{1}{2}m_Tv_T$$KE_B=\frac{1}{2}(900)(3.5)^2+\frac{1}{2}(1100)(2)^2=5512.5+2200=7712.5J$

Then the kinetic energy after the collision

$KE=\frac{1}{2}(900)(2)^2+\frac{1}{2}(1100)(2.5)^2=1800+3437.5=5237.5$

then

$7712.5-5237.5=2475\text{ J}$

the energy that was converted to heat was 2475J