a man throws a rock horizontally off a building with an initial velocity of 22.4 m/s. it hits the ground 91.6 m from the building. how tall is the building? (positive value)

91.6 m / 22.4 m/s = 4.09s is the time it takes to hit the ground. Call it T.

(1/2) g T^2 = height, H
Solve that for H

To solve this problem, we can use the kinematic equation that relates the horizontal distance, initial velocity, and time of motion.

The equation is:
d = v*t

Where:
d is the horizontal distance traveled by the rock
v is the initial velocity of the rock
t is the time of motion

In this case, the distance traveled horizontally by the rock (d) is given as 91.6 m, and the initial velocity (v) is given as 22.4 m/s. We need to find the time of motion (t) to solve the problem.

Since the rock is thrown horizontally, there is no vertical acceleration. Therefore, the time taken for the rock to hit the ground is the same as the time it would take to fall vertically from the height of the building.

We can use the equation for vertical motion:
h = (1/2) * g * t^2

Where:
h is the height of the building
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time of motion

Since we are solving for height (h), we rearrange the equation to solve for t:
t = sqrt(2h/g)

Substituting this value of t into the horizontal distance equation, we get:
91.6 m = 22.4 m/s * sqrt(2h/g)

Now, we can solve for the height (h).

1. First, square both sides of the equation.
(91.6 m)^2 = (22.4 m/s * sqrt(2h/g))^2

2. Simplify the right side of the equation.
(91.6 m)^2 = (22.4 m/s)^2 * (2h/g)

3. Divide both sides of the equation by (22.4 m/s)^2.
(91.6 m)^2 / (22.4 m/s)^2 = 2h/g

4. Multiply both sides of the equation by g.
g * (91.6 m)^2 / (22.4 m/s)^2 = 2h

5. Simplify the left side of the equation by substituting the value of g.
(9.8 m/s^2) * (91.6 m)^2 / (22.4 m/s)^2 = 2h

6. Calculate the value on the left side of the equation.
(9.8 m/s^2) * (91.6 m)^2 / (22.4 m/s)^2 ≈ 392.26 m^2

7. Divide both sides of the equation by 2 to solve for h.
h ≈ (9.8 m/s^2 * (91.6 m)^2 / (22.4 m/s)^2) / 2

8. Simplify the right side of the equation.
h ≈ (392.26 m^2) / 2

9. Calculate the value of h.
h ≈ 196.13 m

Therefore, the height of the building is approximately 196.13 meters.