A grapefruit, thrown horizontally at 15.2 m/s from the top of a tower that stands on level ground, lands 38.1 m from the base of the tower. Neglecting air resistance, what is the height (in meters) of the tower?

To determine the tower's height, time of flight was calculated using horizontal velocity and distance. The height was found using the time of flight and the acceleration due to gravity, resulting in a height of approximately 30.625 m.

Explanation:

To find the height of the tower from which the grapefruit was thrown, we will use the physics concepts of projectile motion. Since air resistance is neglected, two key motions are independent of each other: horizontal motion at a constant velocity and vertical motion under the influence of gravity.

First, we calculate the time of flight of the grapefruit. Given that the horizontal velocity (vx) is 15.2 m/s and the horizontal distance (dx) is 38.1 m, we can find the time (t) it was in the air using the equation:

dx = vx * t

t = dx / vx

t = 38.1 m / 15.2 m/s = 2.5 s

Now, we use the time of flight to calculate the height of the tower using the formula for vertical displacement under constant acceleration due to gravity (g = 9.8 m/s2):

h = 1/2 * g * t2

h = 1/2 * 9.8 m/s2 * (2.5 s)2

h = 1/2 * 9.8 m/s2 * 6.25 s2

h = 30.625 m

Therefore, the height of the tower is approximately 30.625 m.