Question
A projectile is fired from a cliff 300 m high with an initial velocity of 400 m/s. If the firing angle is 30 degrees from the horizontal, compute the horizontal range of the projectile.
Answers
Horizontal problem:
u = 400 cos 30 forever
range = u t
where t is the time from the vertical problem
Vertical problem:
Hi = 300 meters
Vi = 400 sin 30 = 200 m/s
v = Vi - 9.81 t
h = Hi + Vi t - 4.9 t^2
0 = 300 + 200 t - 4.9 t^2
solve that quadratic for t (the positive root, not the one that occurs inside the virtual cliff on the way up)
Use that time in the air in the horizontal problem to get range.
u = 400 cos 30 forever
range = u t
where t is the time from the vertical problem
Vertical problem:
Hi = 300 meters
Vi = 400 sin 30 = 200 m/s
v = Vi - 9.81 t
h = Hi + Vi t - 4.9 t^2
0 = 300 + 200 t - 4.9 t^2
solve that quadratic for t (the positive root, not the one that occurs inside the virtual cliff on the way up)
Use that time in the air in the horizontal problem to get range.
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