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science
Maximum Height:
The maximum height is reached when u
y
= 0. Using this we can rearrange the velocity equation to find the time it will take for
the object to reach maximum height
t
h
= (u • sinθ) / g
where t
h
stands for the time it takes to reach maximum height. From the displacement equation we can find the
maximum height
h = (u2 • sin2θ) / (2 • g)
0
Y
X
Example Problems:
A small rocket is launched at a 30 degree angle at 25 m/s.
1) What is the maximum height reached by the rocket?
The formulas we need to solve this problem are the following:
• u
x
= u0 • cosθ
• u
y
= u0 • sinθ – (g • t)
• g = 9.8 m/s2
At its maximum height, u
y
= u0 • sinθ – (g • t) = 0
First, solving for t:
t = (u0 • sinθ) / g
t = (25 • sin 30) / 9.8
t = 1.28 seconds
Now solve for y:
y = u • t • sinθ – 0.5gt2
y = (25 • 1.28 • sin 30) – (0.5 • 9.8 • 1.282)
y (max) = 7.97 m
The Science of Projectile Motion
θ
Range (R)
θ
Maximum Height (H)
u
x
= u0 • cosθ
u
y
= u sinθ
u
u
x
= u cosθ
u
u
x
= component of velocity along x – axis, a
x
= acceleration along x – axis = 0
u
y
= component of velocity along x – axis, ay = acceleration along y – axis = -g