Question

At what speed do a bicycle and its rider, with a combined mass of $100kg$, have the same momentum as a $1500kg$ car traveling at $5.0m/s$?

Short answer

$v=75m/s$

Step-by-step solution

Given information  

We need to find the speed of a bicycle and its rider.

Simplify  

Objects with mass $m$and speed $s$have momentum $p$, which is the product of mass and speed. y. A large mass or large velocity has large momentum. The momentum is given by equation in the form

$p=mv\left(1\right)$

$m_{car}=1500kg$is mass of the car and velocity is $v_{car}=5.0m/s$.To get the momentum of the car using equation $\left(1\right)$and putting the values for $1500kgand5.0m/s$.

localid="1649419885283" $$\begin{gathered} p_{car}=m_{car}{v}_{car} \\ =(1500kg)(5.0m/s) \\ =7500kg\times m/s \end{gathered}$$

The bicycle and rider have a mass $m=100$with speed $s$.and its equal to the momentum of the car.

Using equation $\left(1\right)$to get $v$of the bicycle and rider

localid="1649340404793" $v=\frac{p_{car}}{m}\left(2\right)$

After putting the values for $m=100kgand{p}_{car}$into equation $\left(2\right)$to get $v$

localid="1649419873774" $$\begin{gathered} v=\frac{p_{car}}{m} \\ =\frac{7500kg\times m/s}{100kg} \\ =75m/s \end{gathered}$$