A wagon loaded with gold (combined mass of 300 kg) rolls/slides down in an incli

Question

A wagon loaded with gold (combined mass of 300 kg) rolls/slides down in an incline of length 50m, which makes an angle of 6 degree with the . The cart starts from rest at the top of the incline.

a) Use kinematics to find the speed of the wagon at the bottom of the incline.

The wagon then continues on a level frictionless road. When the wagon is at a distance of 40m from a cliff, two thiefs (mass 60kg and 75kg), hiding in a tree branch above the wagon, simultaneously jump onto the wagon.

b) if they land vertically, and need 5 seconds to grab all the gold and jump off the wagon again, will they make it before the wagon again, will they make it before the wagon goes over the cliff? You may assume that their shoes experience enough friction with the surface of the wagon, so they do not slide.

USE IMPULSE-MOMENTUM APPROACH

Explanation / Answer

At the base of the incline, potential energy was changed to kinetic so

1/2 mv^2= mgh

1/2 *300*v^2= 300*9,8 * 50 sin6

Solving for v we get 10.121 m/s

When the two people get on the wagon momentum is conserved so

10.121 *300 = (300+60+75) vf

Solving for vf we get 6.98 m/s

So since 6.98*5= 34.9 and they are 40m from the cliff when they jump on, they have time to jump off.

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