A child of mass 30 kg skates down from the top of a ramp having a constant slope of 15°. The child’s speed increases from 1.5 ms−1 to 3.0 ms−1 as she reaches the bottom of the ramp. A force of kinetic friction of magnitude 50 N opposes her motion. Determine the length of the ramp. Take g = 10 ms−2.
The moving force is mg*sin 15 = 300 sin15 = 77.65 N, the resultative force that causes the motion downward is 77.65 - 50= 27.65 N. The acceleration is F/m = 27.65/30 =0.92 m/s2. According equations of the motion h = h0 + v0t + at2/2 v = v0 + at, where v = 3m/s, v0 = 1.5 m/s, h0 = 0, a = 0.92 m/s2. t = (v-v0)/a = (3-1.5)/0.92 = 1.63 s. Thus h = 1.5*1.63 + 0.92* 1.632/2 = 3.67 m.