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 to two significant figures and include the appropriate units.

Answer 1

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

(7.2m/s)² = Vf² + 2*9.8m/s²*1m

Vf = 5.678 m/s

Now we have the launch velocity, and we know the launch angle = 30º

Vertically, Vy = Vf*sin? = 5.678m/s * sin30º = 2.839 m/s

s = So + Vy*t + ½at²

0 = 1m + 2.839m/s*t - 4.9m/s²*t²

t = 0.9897 s ? time of flight

Then horizontally we have

x = Vx*t = Vf*cos?*t = 5.678m/s * cos30º * 0.9897s = 4.9 m ?