Problem 94P

While sitting on a tree branch 10.0 m above the ground, you drop a chestnut. When the chestnut has fallen 2.5 m, you throw a second chestnut straight down. What initial speed must you give the second chestnut if they are both to reach the ground at the same time?

Solution 94P

Step 1 of 4:

Consider we are dropping a chestnut from a branch of a tree at a height. The chestnut reaches 2.5 m from the branch and we throwing another chestnut with an initial speed and both hit the ground at the same time. We are going to find the initial speed of the second chestnut.

The motion of the first chestnut is free fall under the action of gravity. We need to find the first chestnut’s time to reach the ground from the 2.5 m from the branch of the tree.

The height of the tree to ground h = 10 m

The height from the branch h1 = 2.5 m

The acceleration due to gravity g = 9.81 m/s2

The initial speed of the second chestnut = v02