Final answer:
To determine the additional time for the ball to pass the tree branch on its way down, kinematic equations for free fall are used with given values: initial velocity of 15.0 m/s and a gravitational acceleration of 9.8 m/s². The time is calculated for the ball's ascent to 7.00 m and is then doubled to account for the symmetric trajectory of the ball's descent.
Step-by-step explanation:
To evaluate the required time for the ball to pass the tree branch on its way back down, we need to use the kinematic equations for free fall. We need the initial velocity (Vo), the acceleration due to gravity (g), and the height (h) the ball passes when going up.
The initial velocity (Vo) of the ball is given as 15.0 m/s, the acceleration due to gravity (g) is approximately 9.8 m/s² (downward), and the height at which it passes the tree branch on its way up is 7.00 m.
On its way up, the ball is decelerating due to gravity by 9.8 m/s² until it reaches its highest point where its velocity becomes 0 m/s. We will now calculate the time it takes to reach the height of 7.00 m from the ground.
- Use the kinematic equation h = Vo * t - 0.5 * g * t² to find t.
We solve this quadratic equation for t and find the time it takes to reach 7.00 m. However, since the ball needs to return to this height, we must consider its symmetric trajectory. Therefore, the total time that the ball will take to reach this point again on the way down will be twice the time it took to get to 7.00 m the first time.