Final answer:
The ball will reach a height of approximately 10.29 meters on the moon when thrown with a velocity of 4.1 m/s.
Step-by-step explanation:
To determine how high the ball will reach on the moon, we can use the formula:
Final Velocity^2 = Initial Velocity^2 + 2 * Acceleration * Distance
Since the ball is thrown straight up, the final velocity at the highest point will be 0 m/s. The initial velocity is 4.1 m/s. The acceleration can be calculated as 1/6 of the acceleration due to gravity on Earth.
By substituting these values into the formula, we can solve for the distance:
0^2 = 4.1^2 + 2 * (1/6 * 9.8) * Distance
Simplifying the equation, we have:
(1/6 * 9.8) * Distance = 4.1^2
(1/6 * 9.8) * Distance = 16.81
Distance = 16.81 / (1/6 * 9.8)
Distance = 16.81 / 1.633
Distance ≈ 10.29 meters
Therefore, the ball will reach a height of approximately 10.29 meters on the moon.