Question

How much momentum does the woman's cart have before the collision? How much momentum does the man's cart have before the collision? What is the carts momentum once they stick together? What is the speed of the carts after the collision?

A woman pushes her 56 kg shopping cart at 2.8 m/s to the west, while a man pushes his 80 kg shopping cart north at 5.4 m/s. Neither shopper is paying attention and their carts hit and stick together.

Answer 1

Have a look if it is understandable BUT check my maths.

Explanation:

The woman's momentum before will be: `56*2.8=156.8kgm/s`
The man's momentum before will be: `80*5.4=432kgm/s`
and we can evaluate the situation after as:

Rearranging:
`V_x=(56*2.8)/(56+80)=1.15m/s`
`V_y=(80*5.4)/(56+80)=3.17m/s`
So the modulus of the velocity/speed of the entangled carts will be:
`V_("carts")=sqrt(V_x^2+V_y^2)=sqrt(1.15^2+3.17^2)=3.37m/s`
at `theta=arctan(V_y/V_x)=arctan(3.17/1.15)=70.06^@`

Along this direction the momentum of the entangled carts will be: `p_("carts")=(80+56)*3.37=458.32kgm/s`