Peter decides to jump a gorge using a skateboard. The gorge is 60 m wide and Peter uses a 1.5 m high ramp inclined at 25 degrees. What speed does he need in order to get to other side?

Question

Peter decides to jump a gorge using a skateboard. The gorge is 60 m wide and Peter uses a 1.5 m high ramp inclined at 25 degrees. What speed does he need in order to get to other side?

Answer 1

Use the kinematic equation Δx or Δy = v_o t + 1/2 a t². I'm assuming a = -g = -9.8 m/s². Δx is given as 60 m, while Δy is implied to be a drop of 1.5 m. v_o is the appropriate component of initial velocity v, the unknown.

Δx = 60 = (v cos 25) t + 0 (no horizontal acceleration) so the combination vt = 60/(0.9063) = 66.20.

Δy = -1.5 = (v sin 25) t - 4.9 t² yields 4.9 t² = vt (0.4226) + 1.5 = 29.48. Then t² = 6.016, t = 2.453, and the needed speed v = 66.20/2.453 = 27 m/s.