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

• garcia1
In summary, on Earth a person can jump a maximum horizontal distance of 4m using a 45◦ projectile angle and the acceleration of gravity is 9.8 m/s^2. On the Moon, where the free-fall acceleration is g/6, the person's maximum range would be 24m. This can be proven by using kinematics equations and finding that the range is inversely proportional to the gravity.
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 ?

## 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.

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?

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!

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?

You are on the right track with using kinematics equations to solve this problem. To find the maximum range of a jump on the moon, we can use the equation for horizontal displacement:

d = v0x * t

Where d is the horizontal displacement, v0x is the initial horizontal velocity (which can be found using the given projectile angle of 45 degrees), and t is the time of flight.

To find the time of flight, we can use the equation for vertical displacement:

h = v0y * t - 1/2 * g * t^2

Where h is the maximum height reached during the jump, v0y is the initial vertical velocity (which can be found using the given projectile angle of 45 degrees and the free-fall acceleration of the moon, g = 1.6 m/s^2), and t is the time of flight.

We can rearrange this equation to solve for t:

t = (v0y ± √(v0y^2 + 2gh)) / g

Since we want to find the maximum range, we will use the positive solution for t.

Substituting this value of t into the equation for horizontal displacement, we get:

d = v0x * [(v0y + √(v0y^2 + 2gh)) / g]

Now we can plug in the values for v0x and v0y and solve for d:

d = (v0 * cos(45)) * [(v0 * sin(45) + √((v0 * sin(45))^2 + 2 * 1.6 * h)) / 1.6]

Simplifying this equation, we get:

d = 1.25 * [(1.25 + √(1.5625 + 3.2 * h))]

To find the maximum range, we need to find the value of h that will result in the largest possible value for d. This occurs when the term inside the square root is equal to 0, which means that the maximum height reached during the jump is 0. This makes sense, as the maximum range will occur when the person jumps at a 45 degree angle and lands at the same height they started at.

Therefore, the maximum range on the moon would be:

d = 1.25 * [(1.25 + √(1.5625 +

## What is the formula for finding the max range of a jump on the moon using kinematics?

The formula for finding the max range of a jump on the moon using kinematics is: R = (V^2 * sin2θ)/g, where R is the range, V is the initial velocity, θ is the angle of the jump, and g is the acceleration due to gravity on the moon.

## How does the moon's gravity affect the max range of a jump?

The moon's gravity affects the max range of a jump by decreasing the acceleration due to gravity (g) compared to that on Earth. This means that an object will have a longer hang time and therefore a longer range on the moon.

## What factors affect the max range of a jump on the moon?

The factors that affect the max range of a jump on the moon include the initial velocity, angle of the jump, and acceleration due to gravity on the moon. Other factors such as air resistance and the mass of the jumper may also have some impact.

## Can a person jump farther on the moon than on Earth?

Yes, a person can jump farther on the moon than on Earth since the moon's lower gravity allows for a longer hang time and therefore a longer range. However, other factors such as the strength and technique of the jumper may also play a role.

## How can the max range of a jump on the moon be calculated experimentally?

To calculate the max range of a jump on the moon experimentally, a person can perform a series of jumps at different initial velocities and angles while measuring the distance traveled. The data can then be used to plot a graph and find the maximum range using the formula R = (V^2 * sin2θ)/g.

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