The drawing shows a skateboarder moving at 5.4 m/s along ahorizontal section of
ID: 1283718 • Letter: T
Question
The drawing shows a skateboarder moving at 5.4 m/s along ahorizontal section of a track that is slanted upward by 48above the horizontal at its end, which is 0.40 m above the ground.When she leaves the track, she follows the characteristic path ofprojectile motion. Ignoring friction and air resistance, find themaximum height H to whichshe rises above the end of the track.
The drawing shows a skateboarder moving at 5.4 m/s along ahorizontal section of a track that is slanted upward by 48above the horizontal at its end, which is 0.40 m above the ground.When she leaves the track, she follows the characteristic path ofprojectile motion. Ignoring friction and air resistance, find themaximum height H to whichshe rises above the end of the track.
The drawing shows a skateboarder moving at 5.4 m/s along ahorizontal section of a track that is slanted upward by 48 above the horizontal at its end, which is 0.40 m above the ground.When she leaves the track, she follows the characteristic path ofprojectile motion. Ignoring friction and air resistance, find themaximum height H to whichshe rises above the end of the track.Explanation / Answer
Let M = mass of the skateboarder,
v1 = her speed at the point where she leaves the track
By conservation of energy,
1/2 Mv^2 = 1/2 Mv1^2 + Mgh
Dividing by M,
1/2 v^2 = 1/2 v1^2 + gh
Multiplying by 2,
v^2 = v1^2 + 2gh
v1^2 = v^2 - 2gh
v1^2= 5.4^2 - 2*9.8*0.4
v1^2 = 21.32 m^2/s^2
When she leaves the track, then she follows projectile path with initial speed v1, launch angle 48 deg and maximum height H.
H = v1^2 sin^2(48 deg)/(2g)
Or H = 21.32 * 0.74^2/(2*9.8)
H= 0.5956 m
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