Solve Momentum Problem: Find Bullets/Sec Needed for Cart to Reach 19m/s

[pureouchies4717]

hey guys. here's the problem:

A 20 g bullet is shot at a cart that is 200 kg. The cart is on a frictionless surface and is able to move freely. The bullet travels at 400m/s and bounces back with 200m/s after the collision. The design objective is for the cart to reach a speed of 19.0 m/s in 20.0 s. You need to tell them how many bullets to fire per second from the machine gun.

heres what i tried:

p(bullet)=mv
p= 8 (initially)

p(bullet)=mv
= 4 (after impact)

the bullet exerted a momentum of 4 onto the cart.

p(cart)= mv
4= 200v
v=.02m/s after getting shot at by one bullet

19/.02= 950 bullets that need to be fired in order for the car to move at 19m/s

950 bullets/20= 47.5 bullets per second

however, this is wrong

 

[lightgrav]

Momentum is a VECTOR quantity.
the direction after bouncing off the cart is negative,
so the momentum transferred from one bullet to cart is 12 Ns.
(momentum is conserved, so it is transferred, not exerted).

 

[pureouchies4717]

Momentum is a VECTOR quantity.
the direction after bouncing off the cart is negative,
so the momentum transferred from one bullet to cart is 12 Ns.
(momentum is conserved, so it is transferred, not exerted).

thank you :!)