A ball is thrown horizontally at 12.2 m/s from the roof of a building and lands 21.0 m from the base of the building. How high is the building?

Xo = 12.2 m/s.

Range = 21 m.

Range = Xo * Tf = 21 m.
12.2 Tf = 21
Tf = 1.72 = Fall time.

h = 0.5g*Tf^2 = 4.9 * 1.72^2 = 14.5 m.

Well, let's do some calculations, shall we? If the ball is thrown horizontally, then its vertical velocity is initially zero. We can use the equation d = v_i * t + (1/2) * a * t^2, where d is the vertical displacement, v_i is the initial vertical velocity, t is the time, and a is the acceleration. Since the ball is falling vertically, we'll take a to be 9.8 m/s^2 (the acceleration due to gravity).

Now, let's solve for the time it takes for the ball to fall vertically from the roof to the ground. We know that the horizontal distance traveled (21.0 m) is equal to the horizontal velocity (12.2 m/s) multiplied by the time (t). So, t = 21.0 m / 12.2 m/s = 1.72 s.

Next, we can calculate the vertical displacement using the equation d = v_i * t + (1/2) * a * t^2. Since the initial vertical velocity is zero, we're left with d = (1/2) * a * t^2, which simplifies to d = (1/2) * 9.8 m/s^2 * (1.72 s)^2.

Doing the math, we find that the vertical displacement is approximately 15.9976 m. Therefore, the height of the building is approximately 16 meters.

But hey, why did the ball bring a ladder to the party? Because it wanted to "rise" to the occasion!

To find the height of the building, we need to determine how long the ball is in the air. We can use the formula:

Time (t) = Distance (d) / Velocity (v)

In this case, the distance traveled horizontally (d) is 21.0 m, and the velocity (v) horizontally is 12.2 m/s. So:

t = 21.0 m / 12.2 m/s
t ≈ 1.72 s

Now that we know the time, we can find the height of the building using the vertical motion formula:

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

where g is the acceleration due to gravity and is approximately equal to 9.8 m/s^2.

h = (1/2) * 9.8 m/s^2 * (1.72 s)^2
h ≈ 15.8 m

Therefore, the height of the building is approximately 15.8 meters.

A ball is thrown horizontally fron the roof of a building 7.5 tall and lands 9.5m from the base. What was the balls initial speed?

you're stupid