( If a person can jump a maximum horizontal distance (by using a 45° projection angle) of 1.33 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?

Answer 1

Let us assume the shape of the parabolic path will be the same.

Then compare heights reached
v at top = 0 = Vi - g t
so t = Vi/g
so t on moon = 6 * t on earth
Right here you can say it will spend six times as long above soil so goes six times as far since horizontal velocity is the same for both and constant.
h = Vi t - (1/2) g t^2
hmoon = 6 Vi t -(1/2)(g/6)(36 t^2)
or
hmoon = 6 Vi t - 3 g t^2
but t = Vi/g
so h = Vi^2/g -.5 g Vi^2/g^2
h = .5 Vi^2/g
h moon = 3 Vi^2/g
so
height moon = 6 * height earth and distance moon = 6 times distance earth

Answer 2

A 2.00 m tall basketball player is standing on the floor 10.0 m from the basket, as in the figure. If he shoots the ball at a 40.0° angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoop without striking the back board? The height of the basket is 3.05 m