# A 200 g hockey puck is launched up a metal ramp that is inclined at a 30° angle. The coefficients of static and kinetic friction between the hockey puck and the metal ramp are μs = 0.40 and...

A 200 g hockey puck is launched up a metal ramp that is inclined at a 30° angle.

The coefficients of static and kinetic friction between the hockey puck and the metal ramp are

*μ*s = 0.40 and *μ*k = 0.30,respectively. The puck's initial speed is 63 m/s. What vertical height does the puck reach above its starting point?

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### 1 Answer

You need to use the following equation to find the vertical height such that:

`v_i = sqrt(2*a*h) => v^2_i = 2*a*h => h = (v^2_i)/(2a)`

`h_v= h*sin 30^o`

d represents the vertical height

a represents the acceleration of the hockey puck travelling on inclined ramp

`v_i` represents the initial speed

The problem provides the value of initial speed and you may find acceleration such that:

`a = -g(mu_k*cos theta + sin theta)`

`a = -9.8(0.3*cos 30^o + sin 30^o)`

`a = -7.446 m/s^2`

Substituting -7.446 for a yields:

`h = -(63^2)/(2*(-7.446)) => h = 3969/14.892 => h = 266.518`

`h_v= 266.518*sin 30^o =>h_v = 133.259 m`

**Hence, evaluating the vertical height the hockey puck reaches above its starting point yields `h_v = 133.259 m` .**