A skateboarder shoots off a ramp with a velocity of 6.7 m/s, directed at an angl

Question

A skateboarder shoots off a ramp with a velocity of 6.7 m/s, directed at an angle of 57° above the horizontal. The end of the ramp is 1.3 m above the ground. Let the x axis be parallel to the ground, the +y direction be vertically upward, and take as the origin the point on the ground directly below the top of the ramp.
(a) How high above the ground is the highest point that the skateboarder reaches?
(b) When the skateboarder reaches the highest point, how far is this point horizontally from the end of the ramp?

Explanation / Answer

given that initial vertical velocity of the skateboarder uy = 6.7 m/s(sin570) vertical acceleration g = 9.8m/s2
let the skateboarder reach a height h above the end of theramp u = 6.7 m/s (sin570) and final velocity v = 0 from the kinematic equation    v2 - u2 = -2 gh          v2 = u2 + 2 gh           0  =(6.7 m/s(sin570) )2 - 2 ( 9.8 m/s2 ) h            h = 1. 61 m
the highest point is 1.3 m +1. 61 m = 2.91 m above the ground
time taken to reach the highest point = t from the kine matic equation     v = u - gt      0=6.7 m/s(sin570) - 9.8 m/s2 t      t = 0.57 s
initial horizontal velocity u x=6.7 m/s(cos 570) horizontal acceleration=0 distance traveled in 0.57 s horizontally d =6.7 m/s(cos570) 0.57 s                                                               = 2.07
the highest point is 2.07 m from the end of the ramp vertical acceleration g = 9.8m/s2
let the skateboarder reach a height h above the end of theramp u = 6.7 m/s (sin570) and final velocity v = 0 from the kinematic equation    v2 - u2 = -2 gh          v2 = u2 + 2 gh           0  =(6.7 m/s(sin570) )2 - 2 ( 9.8 m/s2 ) h            h = 1. 61 m
the highest point is 1.3 m +1. 61 m = 2.91 m above the ground
time taken to reach the highest point = t from the kine matic equation     v = u - gt      0=6.7 m/s(sin570) - 9.8 m/s2 t      t = 0.57 s
initial horizontal velocity u x=6.7 m/s(cos 570) horizontal acceleration=0 distance traveled in 0.57 s horizontally d =6.7 m/s(cos570) 0.57 s                                                               = 2.07
the highest point is 2.07 m from the end of the ramp

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