"You can jump 2 feet vertically on Earth. Figure out how high you would be able to jump on the Moon, where acceleration due to gravity is ⅙ that of Earth. Assume you launch upwards with the same speed on the Moon as you do on the Earth."

I've already measured how high I can jump and the velocity of the question but I am stuck on this part- It has been narrowed down.

kinetic energy at planet surface = potential energy at max height

(1/2) m v^2 = m g h

h = v^2/2g

so if g is g earth/6 then the height is h earth * 6

STOP DA CAP

To figure out how high you would be able to jump on the Moon, you need to consider the difference in acceleration due to gravity between the Moon and Earth.

On Earth, the acceleration due to gravity is approximately 9.8 m/s². Given that you can jump 2 feet vertically on Earth, which is equivalent to 0.6096 meters, we can consider this as the initial vertical height you achieve when jumping.

Now, let's move on to calculating the velocity with which you launch upwards. Since you mentioned that you launch upwards with the same speed on the Moon as you do on Earth, this means that the initial upward velocity on both Earth and Moon is the same.

Using the standard laws of physics, we can calculate the initial velocity (v) using the equation: v = √(2gh), where "g" is the acceleration due to gravity and "h" is the initial vertical height.

Plugging in the values for Earth:
v = √(2 * 9.8 m/s² * 0.6096 m) = 3.134 m/s

Since the acceleration due to gravity on the Moon is 1/6th of that on Earth, the acceleration due to gravity on the Moon is 1/6 * 9.8 m/s² = 1.6333 m/s².

Using the same equation for the Moon but with the Moon's acceleration due to gravity:
v = √(2 * 1.6333 m/s² * h_moon)

To find the height you would be able to jump on the Moon, we need to calculate the value of "h_moon" (initial vertical height on the Moon).

Let's equate both velocities on Earth and Moon:
3.134 m/s = √(2 * 1.6333 m/s² * h_moon)

Squaring both sides of the equation:
(3.134 m/s)² = 2 * 1.6333 m/s² * h_moon

9.809 m²/s² = 3.2666 m/s² * h_moon

Dividing both sides of the equation by 3.2666 m/s²:
h_moon = 9.809 m²/s² / 3.2666 m/s² ≈ 3.001 m

Therefore, on the Moon, where the acceleration due to gravity is 1/6th that of Earth, you would be able to jump approximately 3.001 meters (or around 9.84 feet) vertically.

Important note: It's worth mentioning that this calculation assumes a simplified scenario with no air resistance or other factors that could affect the real-life situation.