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On planet Arcon, the maximum horizontal range of a projectile launched at 10 m/s is 20 m. What is the acceleration of gravity on this planet?

a) 2.5 m/s²
b) 5.0 m/s²
c) 7.5 m/s²
d) 10.0 m/s²

1 Answer

3 votes

Final answer:

The acceleration of gravity on planet Arcon is 5.0 m/s². Therefore, the correct answer is option b) 5.0 m/s²

Step-by-step explanation:

To find the acceleration of gravity on planet Arcon, we can use the formula for the maximum horizontal range of a projectile:

R = (v² * sin(2θ)) / g

Where R is the range, v is the initial velocity, θ is the launch angle, and g is the acceleration of gravity. We're given that the maximum range is 20m and the initial velocity is 10m/s. We can rearrange the formula to solve for g:

g = (v² * sin(2θ)) / R

Plugging in the values, we get:

g = (10² * sin(2 * 45°)) / 20

Simplifying, we find that the acceleration of gravity on planet Arcon is 5.0 m/s².

To determine the acceleration of gravity on planet Arcon, where the maximum horizontal range of a projectile launched at 10 m/s is 20 m, we use the range formula for projectile motion: R = (v^2 * sin(2θ)) / g, where R is range, v is initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

Here, the maximum range is achieved at a 45° launch angle, meaning sin(2θ) = sin(90°) = 1. Plugging in the values, we get 20 m = (10 m/s)^2 / g, which simplifies to g = (10 m/s)^2 / 20 m = 5.0 m/s². Therefore, the acceleration of gravity on planet Arcon is 5.0 m/s².

Therefore, the correct answer is option b) 5.0 m/s²

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