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