Answer to Question #120990 in Classical Mechanics for Ana

Question

How efficient is a slide when the following occurs. The slide is 30m high and a little boy pushes off and slides down the slide with an initial velocity of 5.0 km/h and reaches the bottom while travelling 20 km/h.

Answer 1

Calculate the theoretical value of final velocity applying conservation of energy principlr:

$mgh+\frac{mv_1^2}{2}=\frac{mv_\text{theor}^2}{2},\\ \space\\ v_\text{theor}=\sqrt{2gh+v_1^2}=24.8\text{ m/s}.$

Since the real final velocity was 20 m, the efficiency is

$\eta=\frac{v_\text{real}}{v_\text{theor}}100\%=\frac{20}{24.8}100\%=81\%.$