Question

A 25-kg child runs at 4.0 m/s and jumps onto a shopping cart and holds on for dear life. The cart has mass 15 kg. Assuming the child rides on the cart after the collision, the speed of the child and shopping cart just after the child jumps on is:_______.
a) zero
b) 2.0 m/s
c) 3.0 m/s
d) 2.5 m/s

Answer 1

Linear momentum (mass x speed) has to be conserved.

-- Momentum before the jump:

(boy's mass) x (boy's speed) = (25 kg) x (4.0 m/s) = 100 kg-m/s

(cart's mass) x (cart's speed) = (15 kg) x (zero) = zero

Total momentum before the jump:  (100 kg-m/s) + (zero) = (100 kg-m/s)

-- Momentum after the jump:

(mass of boy+cart) x (speed of boy+cart) = (40 kg) x (speed)

-- Momentum after the jump = momentum before the jump

(40 kg) x (speed) = 100 kg-m/s

Divide each side by  40 kg:

Speed = (100 kg-m/s) / (40 kg)

Speed = 2.5 m/s  (d)