a) If a person can jump a maximum horizontal distance (by using a 45° projection angle) of 4.17 m on Earth, what would be his maximum range on the Moon, where the free-fall acceleration is g/6 and g = 9.80 m/s2?
b) Repeat for Mars, where the acceleration due to gravity is 0.38g?
R= range
A = angle above horizontal
s = speed
g = acceleration of local gravity
Vi = s sin A = initial speed up
U = s cos A = horizontal speed forever
T = time of flight
T/2 = time for half flight (max height)
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u = s cos A
v = s sin A - g t
top when t = T/2 and v = 0
0 = s sin A - g T/2
T = (2 s /g) sin A
R = u T = (s cos A) T = s cos A * 2 s sin A / g
R = 2 sin A cos A * s^2/g
R = sin 2A * s^2/g
max range when sin 2A = 1 or A = 45 degrees
NO MATTER WHAT G IS
R = s^2/g like period
if g is 1/6 , then R = 6 times as far