Question

You throw a ball straight up with an initial velocity of 15.0 m/s. It passes a tree branch on the way up at a height of 7.00 m. How much additional time will pass before the ball passes the tree branch on the way back down?

a) 0.70 s
b) 1.40 s
c) 2.10 s
d) 2.80 s

Answer 1

The additional time it takes for the ball to pass the tree branch on the way back down is 3.06 s.

Step-by-step explanation:

To determine the additional time it takes for the ball to pass the tree branch on the way back down, we need to understand the motion of the ball. When the ball is thrown straight up, it reaches its maximum height and then falls back down due to the force of gravity.

Since the ball passes the tree branch on the way up at a height of 7.00 m, it will pass the same point on the way down at the same height. The total time it takes for the ball to reach its maximum height and return to the same height is equal to twice the time it takes to reach its maximum height.

Using the equation t = v/g, where t is the time, v is the initial velocity, and g is the acceleration due to gravity, we can calculate the time it takes for the ball to reach its maximum height. Substituting the given values, we have t = 15.0 m/s / 9.8 m/s^2 = 1.53 s.

Therefore, the additional time it takes for the ball to pass the tree branch on the way back down is 2.0 * 1.53 s = 3.06 s.