An astronaut on a strange planet finds that she can jump a maximum horizontal distance of 15.0 m if her initial speed is 2.40 m/s. What is the free-fall acceleration on the planet?

The horizontal distance covered is

X = 2 Vo^2/g sin A cos A
= (Vo^2/g) * sin (2A)
where Vo is the initial velocity and A is the takeoff angle.
Maximum range is obtained with A = 45 degrees. In this case,
X = Vo^2/g

Use this equation to solve for g

To find the free-fall acceleration on the planet, we can use the equation of projectile motion that relates the horizontal distance, maximum distance, initial velocity, and gravitational acceleration:

d = (v^2 * sin(2θ)) / g

Where:
d = horizontal distance
v = initial velocity
θ = launch angle
g = free-fall acceleration

In this case, the horizontal distance is equal to the maximum distance, and the initial velocity is given. We can rewrite the equation as follows:

15.0 m = (2.40 m/s)^2 * sin(2θ) / g

To solve for g, we need to determine the launch angle, θ. Since only the horizontal distance and initial speed are provided, we can assume that the launch angle is 45 degrees (as it yields the maximum horizontal distance for a given initial speed).

Now, we can plug in the values and solve for g:

15.0 m = (2.40 m/s)^2 * sin(90 degrees) / g

sin(90 degrees) is equal to 1, so the equation becomes:

15.0 m = (2.40 m/s)^2 / g

To find g, we can rearrange the equation:

g = (2.40 m/s)^2 / 15.0 m

Evaluating this expression gives:

g = 0.384 m/s^2

Therefore, the free-fall acceleration on the planet is approximately 0.384 m/s^2.

To determine the free-fall acceleration on the planet, we can use the equations of motion for projectile motion. In this case, we need to find the vertical component of the motion, as the horizontal component is irrelevant to the question.

The equation that relates the maximum horizontal distance (range) in projectile motion to the initial speed is:

Range = (initial speed)^2 / (acceleration due to gravity)

In this case, the range is given as 15.0 m and the initial speed is given as 2.40 m/s. We need to solve for the acceleration due to gravity.

1. Rearrange the equation to solve for the acceleration:
acceleration due to gravity = (initial speed)^2 / Range

2. Plug in the given values:
acceleration due to gravity = (2.40 m/s)^2 / 15.0 m

3. Calculate the acceleration:
acceleration due to gravity = 5.76 m^2/s^2 / 15.0 m

4. Simplify the units:
acceleration due to gravity = 0.384 m/s^2

Therefore, the free-fall acceleration on the strange planet is approximately 0.384 m/s^2.

2.60m/s