# A ball thrown horizontally at vi = 26.0 m/s travels a horizontal distance of d = 51.0 m before hitting the ground. From what height h was the ball thrown?

## 51/26=1.9615384615384615384615384615385 secs

h(t)=-4.9(t)²+h(h)
h=4.9(1.9615384615384615384615384615385)²
h=18.85m as the initial height
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## Well, let's see. The ball was thrown horizontally, so it didn't have any vertical velocity at the start. But as it traveled a horizontal distance of 51.0 m before hitting the ground, we know it took some time for it to fall. That means gravity had enough time to work its magic and pull the ball down.

Now, to find out the height h from which the ball was thrown, we can use the formula:

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

where g is the acceleration due to gravity and t is the time it took for the ball to hit the ground. But wait a minute... I just realized something. This question could potentially lead to a misunderstanding. Are we talking about a regular ball or a clown ball? Because with a clown ball, you never know where it might end up! It could go up, down, sideways, or even teleport to a different dimension! So, it's always good to be specific when it comes to clown balls.

But if we assume it's a regular ball and there are no clown shenanigans involved, we can use the formula I mentioned earlier to find the height h. Just remember to use the correct value for the acceleration due to gravity, which is approximately 9.8 m/s^2. Keep in mind that this formula assumes there is no air resistance.

## To find the height from which the ball was thrown, we can use the equation of motion. The horizontal motion does not affect the vertical motion, so we can consider the vertical motion separately.

We know the equation for vertical motion is:

h = vi*t + (1/2)*a*t^2

Where:
h = height from which the ball was thrown (what we want to find)
vi = initial vertical velocity of the ball (0 m/s since the ball was thrown horizontally)
t = time taken for the ball to hit the ground
a = acceleration due to gravity (-9.8 m/s^2)

First, we need to find the time taken for the ball to hit the ground. We can use the equation:

d = vi*t

Where:
d = horizontal distance traveled by the ball before hitting the ground (51.0 m)
vi = initial horizontal velocity of the ball (26.0 m/s)

Rearranging the equation to solve for t:

t = d/vi

Plugging in the values:

t = 51.0 m / 26.0 m/s = 1.96 s

Now we can substitute the value of t in the equation for vertical motion:

h = (0 m/s) * (1.96 s) + (1/2) * (-9.8 m/s^2) * (1.96 s)^2

Simplifying:

h = 0 + (1/2) * (-9.8 m/s^2) * (3.8416 s^2)

h = -4.9 m/s^2 * 3.8416 s^2

h = -18.94 m

The ball was thrown from a height of approximately 18.94 meters.

## To find the height from which the ball was thrown, we can use the equations of motion for projectile motion.

The horizontal motion of the ball is uniform, as there is no acceleration in the horizontal direction. The velocity of the ball in the horizontal direction (Vx) remains constant throughout the motion.

In this case, the initial velocity (vi) of the ball in the horizontal direction is given as 26.0 m/s. The distance traveled (d) by the ball is given as 51.0 m.

Using the equation of motion for horizontal distance, we have:

d = Vx * t

where t is the time of flight of the ball.

Since the ball is thrown horizontally, the initial vertical velocity (Vy) is zero, as there is no initial vertical velocity given. The only force acting on the ball in the vertical direction is gravity, causing it to accelerate downward.

The equation for vertical displacement (h) in terms of initial vertical velocity, time, and acceleration is:

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

where Viy is the initial vertical velocity, g is the acceleration due to gravity (approximated as 9.8 m/s^2), and t is the time of flight.

Since the ball is thrown horizontally, Viy is zero. Therefore, the equation for vertical displacement simplifies to:

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

To find the time of flight (t), we can use the horizontal distance traveled (d) and the horizontal velocity (Vx):

d = Vx * t

Solving for t, we have:

t = d / Vx

Substituting this value of t into the equation for vertical displacement, we can find the height from which the ball was thrown (h):

h = (1/2) * g * (d / Vx)^2

Now we can calculate the height (h). Plugging in the given values:

h = (1/2) * 9.8 * (51.0 / 26.0)^2

Simplifying the equation gives the height from which the ball was thrown.