Finding the max range of a jump on the moon using kinematics

[garcia1]

Homework Statement

A person can jump a maximum horizontal
distance (by using a 45 ◦
projectile angle) of
4 m on Earth.
The acceleration of gravity is 9.8 m/s
2
.
What would be his maximum range on the
Moon, where the free-fall acceleration is g
6 ?
Answer in units of m.

Homework Equations

Kinematics equations

The Attempt at a Solution

All I can think to do is set kinematics equations for the x and y-axis equal to each other by another variable, such as time. This is as far as I can figure out with this problem.

 

[tiny-tim]

hi garcia1!

(have a degree: ° and try using the X² icon just above the Reply box )

from the first part, find the speed at which this person can jump

then use that speed with the Moon's g to find how far he will jump on the Moon …

what do you get? ​

 

[garcia1]

24.0304m/s, by using the fact that vf = 0, and then solving for VoY and getting 6.26m/s. I then plugged this into:

Y = Vy^2 - VoY^2 / (2*-9.81m/s^2 / 6) = 12.01518

Multiplying by two because I used Vf = 0 at the top of the jump, I got 24.0304m. It was right!

 

[tiny-tim]

Woohoo! ​

ok, now have you noticed that the range is inversely proportional to the gravity (24/4 = 6)?

can you prove that, and so avoid all the tedious arithmetic? ​