To determine the total time of travel and the initial velocity of the ball thrown by Gina, we need some additional information. Specifically, we need to know the acceleration due to gravity and any other factors that might affect the ball's motion, such as air resistance.
Assuming we're working in a vacuum and neglecting air resistance, we can use the equations of motion to calculate the time of travel and initial velocity.
The equation for the height reached by an object thrown vertically upward is given by:
h = (v_i^2 - v_f^2) / (2 * a)
Where: h is the height reached (10 m), v_i is the initial velocity, and v_f is the final velocity (which is 0 at the peak of the ball's trajectory). a is the acceleration due to gravity (-9.8 m/s^2).
Plugging in the values we have:
10 = (v_i^2 - 0) / (2 * -9.8)
Simplifying the equation:
-19.6 = v_i^2
Taking the square root of both sides:
v_i ≈ ±4.42 m/s
Since the ball is thrown upward, the initial velocity should be positive:
v_i ≈ 4.42 m/s
Now, to find the total time of travel, we can use the equation:
t = (v_f - v_i) / a
Where v_f is the final velocity and is equal to 0 at the peak of the ball's trajectory.
Plugging in the values:
t = (0 - 4.42) / -9.8
Simplifying the equation:
t ≈ 0.45 s
Therefore, if Gina threw the ball upward and it reached a height of 10 meters, the total time of travel would be approximately 0.45 seconds, and the initial velocity of the ball would be approximately 4.42 m/s.