A tennis ball on Mars, where the acceleration due to gravity is 0.379 of a and air resistance is negligible, is hit directly upward and returns to the same level 6.90 later.
To determine the initial velocity and the height reached by the tennis ball on Mars, we can use the equations of motion for an object in freefall motion.
1. Calculate the time of flight:
Given that the tennis ball returns to the same level after 6.90 seconds, the time of flight is equal to twice the time it takes for the ball to reach its maximum height. So, the time taken for the ball to reach the maximum height is half of 6.90 seconds, which is 6.90/2 = 3.45 seconds.
2. Calculate the initial velocity:
Using the equation of motion for vertical motion, we can find the initial velocity (Vi) by using the following formula:
Vi = gt,
where g is the acceleration due to gravity on Mars, which is 0.379 times the acceleration due to gravity on Earth.
On Earth, g is approximately 9.8 m/s^2. Therefore, on Mars, g equals 0.379 * 9.8 m/s^2 = 3.7222 m/s^2.
So, Vi = (3.7222 m/s^2) * (3.45 s) = 12.8271 m/s (rounded to four decimal places).
3. Calculate the maximum height reached:
To find the maximum height (H), we can use the following equation of motion:
H = Vi*t - (1/2)*g*t^2,
where Vi is the initial velocity, g is the acceleration due to gravity on Mars, and t is the time taken to reach the maximum height.
Plugging in the values we have, we get:
H = (12.8271 m/s) * (3.45 s) - (1/2)*(3.7222 m/s^2)*(3.45 s)^2.
Evaluating this expression, we can find the maximum height reached by the tennis ball on Mars.
Note: Due to rounding errors and slight variations in the given data, the final result may differ slightly.