Question

A skateboarder, starting from the top of a ramp 4,5 m above the ground, skates down the ramp. The mass of the skateboarder and his board is 65 kg
Use the principle of conservation of mechanical energy to calculate the magnitude of the velocity of the skateboarder when he reaches the ground

Answer 1

Answer:

Explanation:

The potential energy (PE) of the skateborder (and board) is given by mgh (mass, gravity acceleration, and height).  Assuming no friction of any kind, the magnitude of the skateboarder's velocity will be the result of converting the potential energy to kenetic energy (KE), (1/2)mv².  

[We only know the magnitude of the velocity since we aren't told in which direction the skateboarder is headed.]

1.  Calculate PE:

mgh

(65kg)*(9.61m/s²)*(4.5m) = 2811 kgm²/s² (Joules)

2.  Calculate Speed from KE

Since we are assuming no friction nor other forces, all of the PE will be converted to KE, so we can write:

PE = (1/2)mv²

2811 kgm²/s² = (1/2)*(65kg)v²

v² = (2811 kgm²/s²)/((1/2)*(65kg))

v² = 86.49 m²/s²

v = 9.3 m/s  :  The magnitude of the velocity.  

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I vote pointing the skateboarder west, where the gold is.  His velocity would be 9.3 m/s West.

Answer 2

Answer:

Kinetic Energy at bottom=2886.5J (when g=9.8m/s²)

OR

2925J (if g=10m/s²)