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

Question

A skateboarder starts up a 1.0-m-high, 30∘ ramp at a speed of 7.2 m/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?
Express your answer with the appropriate units.

bobpursley · Accepted Answer

Her initial KE-topPE=KE at top

1/2 m 7.2^2 - mg*1m=1/2 m vt^2

vt=sqrt(7.2^2-2*9.8)= 5.68m/s

Now how long does it take to fall 1 meter
hf=hi+vi'*t-4.9t^2
0=1+5.68sin30*t-4.9 t^2

solve that for time t using the quadratic equation (or you calculator).

Now, given the time in air, the horizontal distance is
d=5.68*Cos30*timet