An astronaut on a strange planet �nds that she can jump a maximum horizontal distance of 30 m if her

initial speed is 9 m/s. What is the acceleration of gravity on the planet?

θ=45° because maximum distance

R=(Vi²/g)(sin2θ)

g=2.7m/s²

correct?

To determine the acceleration of gravity on the strange planet, we can use the given information about the maximum horizontal distance that the astronaut can jump. The formula for the range (maximum horizontal distance) of a projectile is:

R = (V^2 * sin2θ) / g

where R is the range, V is the initial speed, θ is the launch angle, and g is the acceleration due to gravity.

In this case, the astronaut can jump a maximum horizontal distance of 30 m with an initial speed (V) of 9 m/s. The launch angle (θ) is 45° because it provides the maximum distance. Now, let's rearrange the formula to solve for g:

g = (V^2 * sin2θ) / R

Substituting the given values:

g = (9^2 * sin(2 * 45°)) / 30
g = (81 * sin(90°)) / 30
g = (81 * 1) / 30
g ≈ 2.7 m/s²

Therefore, the acceleration of gravity on the strange planet is approximately 2.7 m/s². So yes, your answer is correct!