A ball thrown horizontally at 21m/s from the roof of a building lands 24m from the base of the building. Now high is the building?

Refer to these equations.

Vx (Horizontal velocity) (21m/s here)
Vx = dx/t
Dx (Horizontal distance) (24m here)
Dx = vx(t)
Dy (Vertical distance) (missing here)
dy=(1/2)(g)t^2

t is just time.
you can use first or second equation to find time. either one works.
21m/s = 24m / t
t = 24/21 = 1.14 seconds

Now put time value to last equation
dy = (1/2)(9.8)1.14^2

dy = 6.36804 or 6.37m

To find the height of the building, we can use the equation for horizontal motion:

d = v * t

where:
d is the horizontal distance traveled by the ball (24 m),
v is the horizontal velocity of the ball (21 m/s),
and t is the time taken for the ball to hit the ground.

Since the ball is thrown horizontally, the vertical velocity is constant and equal to 0 m/s. Therefore, the time taken for the ball to hit the ground can be found using the vertical motion equation:

d = v₀ * t + (1/2) * g * t²

where:
d is the vertical distance traveled by the ball (the height of the building),
v₀ is the initial vertical velocity of the ball (0 m/s),
g is the acceleration due to gravity (approximately 9.8 m/s²),
and t is the time taken for the ball to hit the ground.

Since v₀ = 0 m/s, the equation simplifies to:

d = (1/2) * g * t²

Rearranging the equation to solve for t:

t² = (2 * d) / g

t² = (2 * 24) / 9.8

t² = 4.89795918

Taking the square root:

t ≈ √4.89795918

t ≈ 2.213 seconds

Now we can use the horizontal motion equation to find the height of the building:

d = v * t

d = 21 m/s * 2.213 s

d ≈ 46.47 meters

Therefore, the height of the building is approximately 46.47 meters.

To determine the height of the building, we can use the equation of motion. When the ball is thrown horizontally, the initial vertical velocity is zero.

Let's break it down step by step:

1. The initial vertical velocity (ui) is 0 m/s.
2. The acceleration due to gravity (a) is approximately -9.8 m/s² (assuming downwards as the positive direction).
3. The horizontal velocity (ux) is given as 21 m/s.

Now, we can calculate the time it takes for the ball to hit the ground using the vertical motion equation:

h = ui * t + (1/2) * a * t²

Since ui is 0, the equation simplifies to:

h = (1/2) * a * t²

Rearranging the equation, we get:

t² = (2 * h) / a

t² = (2 * h) / (-9.8)

Next, to determine the time of flight horizontally, we can use the horizontal motion equation:

d = ux * t

Here, d represents the horizontal distance traveled by the ball, which is given as 24 m. Substituting the values, we find:

24 = 21 * t

Simplifying, we get:

t = 24 / 21

Finally, we substitute this value of t into the equation obtained earlier to determine the height of the building:

(24 / 21)² = (2 * h) / (-9.8)

Solving for h, we find:

h = (-9.8 * (24 / 21)²) / 2

Evaluating the equation, we find that the height of the building is approximately 11.37 meters.