Question

An astronaut on a newly discovered planet conducted an experiment to determine the magnitude of the acceleration due to gravity. She stood on a cliff and shot a projectile horizontally at an initial rate of 23 m/s. The cliff was 52 m high, and the projectile traveled 45 m from the cliff before striking the ground. What was the magnitude of the acceleration due to gravity on this planet?

Answer 1

To determine the magnitude of the acceleration due to gravity on the newly discovered planet, we can use the formulas for horizontal and vertical motion. The magnitude of the acceleration due to gravity on this planet is approximately 5.04 m/s².

Step-by-step explanation:

To determine the magnitude of the acceleration due to gravity on the newly discovered planet, we can use the formula for horizontal motion.

Firstly, we need to find the time it takes for the projectile to travel the horizontal distance of 45 m. This can be done using the formula:

distance = velocity × time

45 m = 23 m/s × time

Solving for time, we get:

time = 45 m / 23 m/s = 1.96 s

Next, we can use the formula for vertical motion to find the acceleration due to gravity:

height = (1/2) × acceleration × time^2

52 m = (1/2) × acceleration × (1.96 s)^2

Solving for acceleration, we get:

acceleration = 52 m / ((1/2) × (1.96 s)^2) = 5.04 m/s²

Therefore, the magnitude of the acceleration due to gravity on this planet is approximately 5.04 m/s².