Dan is gliding on his skateboard at 3.00 m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8.00 m/s. Dan's mass is 70.0 kg and the skateboard's mass is 6.00 kg. How fast is Dan going as his feet hit the ground?

The velocity of Dan is 2.57m/s as his feet hit the ground

Explanation:

The impact experience by Dan and the skate board is an elastic collision

Collision is elastic when the kinetic energy is not conserved and if there is rebound after collision

Given that

U= initial velocity of Dan and the skate board 3m/s

M1 =mass of Dan 70kg

M2= mass of Skate board 6kg

V1= final velocity of Dan?

V2= Final velocity of skate board 8m/s

The expression for Dan and the skate board collision can be expressed as

Momentum before impact momentum after impact

(M1+M2)U=M1V1+M2V2

Substituting our data we have

(70+6)3=(70*V1)+(6*8)

228=70V1+48

Solving for V1

228-48=70V1

V1=180/70

V1=2.57m/s