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

Question

A wagon loaded with gold (combined mass of 300 kg) rolls/slides down on an incline of length 50 m , which makes an angle of 6 degrees with the horizontal. The carts 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 frinctionless road. When the wagon is a t a distance of 40m from a cliff, two theifs (mass 60 kg and 75 kg), 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 goes over the cliff? You may assure theat their shoes experiance enough friction with the surface of the wagon, so they do not slide.

Explanation / Answer

A)
here, a = g*sin(6)

= 9.8*sin(6)

= 1.024 m/s^2

v^2-u^2 = 2*a*s

v^2 - 0 = 2*1.024*50

v = sqrt(2*1.024*50)

= 10.12 m/s

B)

here momentum is conserved.

let v is the speed of total system when theives enter
m*u = (m+m1+m2)*v

v = m*u/(m+m1+m2)

= 300*10.12/(300+60+75)

= 7 m/s

distance travelled in 5 seconds, x = 7*5

= 35 m

so, they can make it.

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