A skateboarder starts up a 1.0m high, 30∘ ramp at a speed of 7.5 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?
1 Answer

Strategy: use conservation of energy to find the launch velocity, then basic kinematics.
CoE gives us
initial KE = final KE + final PE
which after dividing through by mass/2 gives
Vi² = Vf² + 2gh
(7.5m/s)² = Vf² + 2*9.8m/s²*1m
Vf = 6.05 m/s
Now we have the launch velocity, and we know the launch angle = 30º
Vertically, Vy = Vf*sinΘ = 6.05m/s * sin30º = 3.03 m/s
s = So + Vy*t + ½at²
0 = 1m + 3.03m/s*t  4.9m/s²*t²
This quadratic has roots at t = 0.24 s ← not possible
and t = 0.86 s ← time of flight
Then horizontally we have
x = Vx*t = Vf*cosΘ*t = 6.05m/s * cos30º * 0.86s = 4.5 m ◄
Hope this helps!