A skateboarder shoots off a ramp with a velocity of 6.5 m/s, directed at an angl
ID: 1764257 • Letter: A
Question
A skateboarder shoots off a ramp with a velocity of 6.5 m/s, directed at an angle of 60° above the horizontal. The end of the ramp is1.5 m above the ground. Let the xaxis be parallel to the ground, the +y direction bevertically upward, and take as the origin the point on the grounddirectly below the top of the ramp. (a) How high above the groundis the highest point that the skateboarder reaches?1 m
(b) When the skateboarder reaches the highest point, how far isthis point horizontally from the end of the ramp?
m
Explanation / Answer
A skateboarder shoots off a ramp with a velocity of 6.5 m/s, directed at an angle of 60° above the horizontal. The end of the ramp is1.5 m above the ground. Let the xaxis be parallel to the ground, the +y direction bevertically upward, and take as the origin the point on the grounddirectly below the top of the ramp. (a) How high above the groundis the highest point that the skateboarder reaches? 1 m maximumheight=u*usin2/2g=6.5*6.5*(sin60)2/2*9.8=1.6167m (b) When the skateboarder reaches the highest point, how far isthis point horizontally from the end of the ramp? range=u*usin2/g=6.5*6.5*sin120/9.8=3.733m half of the range which corresponds to maximumheight=3.733/2=1.866m horizontal distance that corresponds to end of theramp=1.5sin60=1.299m hence the point that corresponds to maximum height is at ahoriontal distance of 1.866-1.299=0.5669m m