Question

Dan is gliding on his skateboard at $4.0\mathrm{m}/\mathrm{s}$. He suddenly jumps backward off the skateboard, kicking the skateboard forward at $8.0\mathrm{m}/\mathrm{s}$. How fast is Dan going as his feet hit the ground? Dan’s mass is $50\mathrm{kg}$ and the skateboard’s mass is $5.0\mathrm{kg}.$

Short answer

The sped of the Dan is $3.6\mathrm{m}/\mathrm{s}.$

Step-by-step solution

Given information

We have given,

$$\begin{gathered} \mathrm{Mass}\mathrm{of}\mathrm{Dan}=50\mathrm{kg} \\ \mathrm{Mass}\mathrm{of}\mathrm{skateboard}=5\mathrm{kg} \\ \mathrm{velocity}\mathrm{of}\mathrm{skateboard}=8\mathrm{m}/\mathrm{s} \end{gathered}$$

We have to find the Dan final speed.

Simplify

According to conservation law of momentum that the initial momentum of the system will be same to the final momentum of the system.

then, we can write

the initial momentum of the system will be given as,

$$\begin{gathered} {\mathrm{P}}_{\mathrm{I}}=({\mathrm{m}}_{\mathrm{Dan}}+{\mathrm{m}}_{\mathrm{Skateboard}})\mathrm{V} \\ {\mathrm{P}}_{\mathrm{I}}=(50\mathrm{kg}+5\mathrm{kg})(4\mathrm{m}/\mathrm{s}) \\ {\mathrm{P}}_{\mathrm{i}}=220\mathrm{kg}\mathrm{m}/\mathrm{s} \end{gathered}$$

then, the final momentum will be,

$$\begin{gathered} {\mathrm{P}}_{\mathrm{F}}={\mathrm{m}}_{\mathrm{Dan}}{\mathrm{V}}_{\mathrm{FINAL}\mathrm{DAN}}+{\mathrm{m}}_{\mathrm{Skateboard}}{\mathrm{V}}_{\mathrm{FINAL}\mathrm{SKATEBIARD}} \\ {\mathrm{P}}_{\mathrm{F}}=(50\mathrm{kg})\mathrm{V}+(5\mathrm{kg}\times 8\mathrm{m}/\mathrm{s})=220\mathrm{kg}\mathrm{m}/\mathrm{s} \\ \mathrm{V}=3.6\mathrm{m}/\mathrm{s} \end{gathered}$$