Question

A skateboarder starts up a 1.0-m-high, 30? ramp at a speed of 7.2m/s . The skateboard wheels roll without friction. At the top, she leaves the ramp and sails through the air.

How far from the end of the ramp does the skateboarder touch down?

Answer 1

Force = mass * acceleration

Initial KE = 0.5 * mass * initial velocity^2 = 0.5 * mass * 7.2^2

Initial PE = mass * g * initial height = mass * 9.8 * 0= 0

Final KE = 0.5 * mass* final velocity^2

Final PE = mass * g* height= mass * 9.8*1 = 9.8

0.5 * mass* final velocity^2 + mass * 9.8 = 0.5 * mass * 7.2^2

divide both sides by mass

0.5 * final velocity^2+ 9.8 = 0.5 * 7.2^2

multiply by 2 on both sides

final velocity^2 + 19.6 = 51.8

final velocity ^2 = 32.2

final velocity = sqrt 32.2 m/s

Initial velocity = V * sin tetha = sqrt 32.2 * sin 30

Time up = ( sqrt 32.2 * sin 30) / 9.8

Final velocity up = 0 m/s

average velocity up = 0.5 * sqrt 32.2 * sin 30

Distance up = (0.5 * sqrt 32.2 * sin 30 )) * [ ( sqrt 32.2 * sin 30) / 9.8] = 0.4099

Distance down = 0.4099 + 1 = 1.4099 m

Now final velocity=?

Final velocity ^2 = 2*9.8*1.4099

final velocity = ( 2*9.8*1.4099)^0.5 = 5.25

Time down = ( final velocity - initial velocity ) / 9.8

time down = 5.25 / 9.8 = 0.535 sec

Total time = sqrt 32.2 * sin 30 ) / 9.8 = 0.289 sec

Horizontal velocity = V * cos tetha = 5.67* cos 30 = 4.91 sec

Horizonyal distance = 5.67 * 0.866 *0.289 =1.419 m