Question

Estimate how much farther a person can jump on the Moon as compared to Earth if the take off

speed and angle are the same? The acceleration due to gravity on the moon is one-sixth what it
is on Earth.

Answer 1

The maximum distance on the Moon is six times higher than on the Earth for the object with the same angle and take off speed.

Step-by-step explanation:

Let us assume , an Object is thrown with initial Velocity u m/s and angle of θ above the horizontal level. The horizontal and vertical velocities are (x,y)

vₓ = v₀cos θ

`v_(y)` = v₀ sinθ

now, the time when the object reaches the maximum height can be calculated from

`v_(y)` = v₀ sinθ - at₀ = 0

t₀ = v₀ sinθ/a

thus, the total time in air is two times higher ; t = 2t₀ = 2 (v₀ sinθ) /a

the maximum distance can be calculated from this equation

X = vₓ t= v₀ cos θ x 2 (v₀ sinθ) /a

it implies x is inversely proportional to a.

we know the acceleration on the Moon is 1/6 th of Earth.the ratio between between maximal distance on the moon and on the earth is 6.