Question

You are standing at the base of a tree, and you want to know how tall it is. You have a ball,

a stopwatch, and a calculator. You toss the ball straight up in the air to almost exactly the
height of the tree, and you time the number of seconds it takes to go up and return to the
ground below. It took 8 seconds from the time the ball left your hand until the time it re-
turned to the ground. You remember that the time going up will be equal to the time com-
ing down. With this in mind, calculate the height of the tree in meters.

Answer 1

To calculate the height of the tree, divide the total time taken by the ball by 2 to find the time taken to reach the highest point. Then, use the equation of motion for an object thrown vertically to find the height of the tree.

Step-by-step explanation:

To calculate the height of the tree, we can use the fact that the time it takes for the ball to go up will be equal to the time it takes for the ball to come back down. Since it took 8 seconds for the ball to go up and come back down, we can divide this time by 2 to find the time it took for the ball to reach the highest point. This gives us a time of 4 seconds.

Using the equation of motion for an object thrown vertically, we can find the height of the tree. The equation is given by:

h = (1/2) * g * t^2

where h is the height of the tree, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time (4 seconds).

Substituting the values into the equation, we have:

h = (1/2) * 9.8 * (4^2)

h = 78.4 m

Therefore, the height of the tree is 78.4 meters.