Calculate the magnitude of the velocity of the rock just before it strikes the ground?
A man stands on the roof of a building that is 15.6 meters high and throws a rock with a velocity of 31.1 m/s at an angle of 26.2 degrees above the horizontal. For this problem, you can ignore air resistance.
A. Calculate the magnitude of the velocity of the rock just before it strikes the ground.
B. Calculate the horizontal distance from the base of the building to the point where the rock strikes the ground.
1 Answers
(a)
By conservation of energy
Ki + Ui = Kf + Uf
1/2m(vi)^2 + mgh = 1/2m(vf)^2 + 0
vf = √((vi)^2 + 2gh) = 35.7 m/s
(b)
In the y direction
s = ut + 1/2at^2
s = vsinθt – 1/2gt^2
-15.6 = 31.1sin26.2°t – 1/2 gt^2
t = 3.66975 s
In the x direction
x = vcosθt = (31.1)cos26.2°(3.66975) = 102 m
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