Question

A child on a sled starts from rest at the top of a 15.0° slope. If the trip to the bottom takes 22.6 s how long is the slope? Assume that frictional forces may be neglected. A child on a sled starts from rest at the top of a 15.0 slope. If the trip to the bottom takes 22.6 s how long is the slope? Assume that frictional forces may be neglected. 648 m 2500 m 324 m 1300 m

Answer 1

Answer:

648 m

Explanation:

Let the length of slope be 'L' m.

Given:

Initial velocity of the child (u) = 0

Angle of inclination of the slope (x) = 15.0°

Time taken to reach the bottom (t) = 22.6 s

Acceleration due to gravity (g) = 9.8 m/s²

No frictional forces act.

Now, acceleration acting on the child along the slope can be determined by resolving the acceleration due to gravity along the slope.

So, acceleration along the slope is given as:

$a_{slope}=g\sin(x)=9.8\sin(15)=2.536\ m/s^2$

Now, use to equation of motion along the slope to find the length of slope.

Therefore,

$L=ut+\frac{1}{2}a_{slope}t^2\\\\L=0+\frac{1}{2}(2.536)(22.6)^2\\\\L=1.268\times 510.76=647.6\approx 648\ m$

Therefore, the slope is 648 m long.

Option (1) is correct.