Question

Dan is gliding on his skateboard at 4.00m/s . He suddenly jumps backward off the skateboard, kicking the skateboard forward at 6.00m/s . Dan's mass is 60.0kg and the skateboard's mass is 7.00kg .
How fast is Dan going as his feet hit the ground?

Answer 1

To solve this problem we will apply the concepts related to the conservation of the Momentum. For this purpose we will define the momentum as the product between mass and velocity, and by conservation the initial momentum will be equal to the final momentum. Mathematically this is,

$m_1u_1+m_2u_2 = m_1v_1+m_2v_2$

Here,

$m_{1,2}$ = Mass of Dan and Skateboard respectively

$u_{1,2}$ = Initial velocity of Dan and Skateboard respectively

$v_{1,2}$ = Final velocity of Dan and Skateboard respectively

Our values are:

Dan's mass

$m_1 = 60kg$

Mass of the skateboard

$m_2 = 7.0kg$

Both have the same initial velocity, then

$u_1= u_2 = 4m/s$

Final velocity of Skateboard is

$v_2 = 6m/s$

Rearranging to find the final velocity of Dan we have then,

$m_1u_1+m_2u_2 = m_1v_1+m_2v_2$

$m_1v_1+m_2v_2 = (m_1+m_2)u_1$

$v_1 = \frac{ (m_1+m_2)u_1 -m_2v_2}{m_1}$

Replacing,

$v_1 = \frac{(60+7)(4)-(7)(6)}{60}$

$v_1 = 3.76m/s$

Therefore Dan will touch the ground at a speed of 3.76m/s