A skateboarder cruising across a smooth, level sidewalk is approaching a pipe gu

Question

A skateboarder cruising across a smooth, level sidewalk is approaching a pipe guardrail. It seems like a good idea for him to jump over the rail and let the skateboard pass under the rail. The mass of the boy is 38.8 kg, the mass of the skateboard is 2.61 kg, the initial cruising speed is +4.82 m/s, and the instant after leaving contact with the board, the boy's velocity relative to the sidewalk is 5.05 m/s, 9.36° above the horizontal. If we ignore the force of friction between the skateboard and the sidewalk, determine the skateboard's velocity relative to the sidewalk at the instant the boy leaves the board.

...........................m/s

Explanation / Answer

Momentum of the system will be conserved before and after the jump.

so, for x axis,

(m+M)u = Mvcos9.36 + mV

=> (2.61+38.8)(4.82) = (38.8)(5.05)cos9.36 + 2.61V

=> 2.61V = 6.265

=> V = + 2.4 m/s

this is the velocity of the skateboard relative to the sidewalk. The positive sign indicates that the board will be traveling in the direction of motion of the skater.

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