Question

A hockey puck is at the top of a 10 m long slippery slope, that makes an angle of 30° to the horizontal and leads down to a flat hockey rink. The hockey puck is struck with a hockey stick giving it a speed of 5 m/s. What is the speed of the hockey when it reaches the bottom of the slope? Assume friction is negligible.
A) 10.5 m/s
B) 8.5 m/s
C) 8.6 m/s
D) 11.1m/s
E) Cannot say without knowing mass of hockey puck

Answer 1

To solve this problem, we will first apply the concepts related to trigonometric relations and then the conservation of energy. By the trigonometric relations we will find the height for the calculation of the potential energy. For the conservation of energy we will give the relationship between the kinetic energy and initial potential with the final kinetic energy. Therefore, first the height by trigonometric relation we have

$h = Lsin\heta$

$h = 10sin30\°$

$h = 5m$

Then by conservation of energy

$E_i = E_f$

$mgh+\frac{1}{2}mv_i^2 = \frac{1}{2}mv_f^2$

Here,

m = mass

g = Gravitational acceleration

v = Velocity

Rearranging to find the final velocity,

$v_f = \sqrt{v_i^2+2gh}$

$v_f = \sqrt{5^2+(9.8*10)}$

$v_f = 11.1m/s$

Therefore the correct answer is D.