Presumbly he can release the ball at the same velocity and kinetic energy on either planet. The potential energy gain at maximum height will be the same. That means the product of height H and g will be the same.
9.8*H(earth) = 3.7*H(mars) = 259 m^2/s^2
H(earth) = 26.4 m
Having said that, I would expect it to be harder to throw a baseball as fast on Mars while wearing a space suit with helmet. Such life-support items are not needed on Earth.
The acceleration due to gravity of mars is 3.7 m/s2. An astronautto throw a tennis ball 70 m upward on mars. How high will he able to throw it on the earth?
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