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 μk = 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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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` .
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