A projectile is launched on level ground at an angle theta from the horizontal w

Question

A projectile is launched on level ground at an angle theta from the horizontal with initial speed v0. It reaches the ground again at a time t and at a location x,y.

a. Find a general expression for the time it takes to rise to the maximum height (your answer must be in terms of theta, v0, and g.

b. Find a general expression for the maximum height relative to a coordinate system located at the initial launch point. (your answer must be in terms of theta, v0, and g)

c. If this projectile is now launched horizontally from a rooftop, 45 meters above the ground, with an initial speed of 10 m/s, find the projectile

Explanation / Answer

A)
H=v0sin?t-1/2gt^2
the projectile reaches its maximum height H.when
vsin?=v0sin?-gt(H)=0 ==>v0sin?=gt(H)
so
t(H)=v0sin?/g
replacing in the first eq.
H=(v0sin?)^2/(2g)

B)
the projectile hits the ground when
t=v0sin?/g+v0sin?/g
the trajectory is symmetrical respect to the vertical axis crossing the point H
so the total fly time is twice the time to reach the max. altitude
t=2v0sin?/g

C)
the total distance R (the range) traveled in x direction is
R=v0cos?t
when
t=2v0sin?/g (fly time)
so
R=(2v0cos?*v0sin?)/g
or
R=v0^2sin(2?)/g

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