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# Newton's Law of Motion - sliding down a slope

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A 20-kg child sits on a 5-kg sled and slides down a 125-meter, 31-degree slope, to the nearest m/s what is his or her speed at the bottom?

https://brainmass.com/physics/acceleration/newtons-law-motion-sliding-down-slope-50473

## SOLUTION This solution is FREE courtesy of BrainMass!

The total mass of the child + sled = 25 Kg, we will consider this as a single mass. The only force acting on the mass when it is at the top of the slope is the force due to gravity which is equal to

F = mg

This acts vertically downwards.

But since he is on an incline, we need the component of this force along the inclined surface. For this we will resolve the downward force mg.

It can be resolved as shown in the figure..

The component is mg Sin31 = 25 * 9.8 * 0.515 = 126.175 Newton

This force creates the acceleration.

acceleration is given by, a = force/mass = 126.175/25 = 5.047 m/s^2

We have the height = 125meter, acceleration = 5.047m/s^2

we need the velocity at the bottom point. For the we will use the formula,

v^2 = v(0) ^2 + 2as

where v(0) is the initial velocity of the boy, which is zero. and S is the distance travelled = 125 meter and a is the acceleration. V is the final velocity

V^2 = 0 + 2 * 5.047 * 125 = 1261.75 m/s

or V = sqrt 1261.75