Answer:
(a) To determine the time it takes for the baseball to reach the highest point in its path, we need to use the equation:
v_f = v_i + a*t
where v_f is the final velocity, v_i is the initial velocity, a is the acceleration, and t is the time.
At the highest point in its path, the baseball will momentarily stop before falling back down to the surface, so its final velocity will be zero. The initial velocity is 30.00 m/s, and the acceleration due to gravity on Mars is 4.00 m/s². Plugging these values into the equation, we get:
0 = 30.00 m/s - 4.00 m/s² * t
Solving for t, we get:
t = 7.50 s
Therefore, it will take 7.50 seconds for the baseball to reach the highest point in its path.
(b) To determine how high the baseball will reach, we need to use the equation:
y_f = y_i + v_it + 1/2a*t²
where y_f is the final height, y_i is the initial height (which we can assume is zero), v_i is the initial velocity, a is the acceleration, and t is the time.
Plugging in the values we know, we get:
y_f = 0 + 30.00 m/s * 7.50 s + 1/2 * 4.00 m/s² * (7.50 s)²
Simplifying this expression, we get:
y_f = 562.50 m
Therefore, the baseball will reach a height of 562.50 meters above the surface of Mars before falling back down.