A200 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 99 m/s. what vertical height does the puck reach above its starting point?

H=1020.12m

Explanation:

From a balance of energy:

  where H is the height it reached, d is the distance it traveled along the ramp and Ff = μk*N.

The relation between H and d is given by:

H = d*sin(30)   Replace this into our previous equation:

From a sum of forces:

N -mg*cos(30) = 0    =>  N = mg*cos(30)   Replacing this:

  Now we can solve for d:

d = 2040.23m

Thus H = 1020.12m

the vertical height reach by the puck is 329.06m

Explanation:

In all the process, the only non-conservative force presented in the problem is the frictional force. Therefore, applying the Mechanical energy conservation:

with:

From the dynamic analysis:

Therefore:

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach