# Solving for Building Height and Time in Horizontal Projectile Motion

• harujina
In summary, the problem involves a ball being thrown horizontally from a building and landing 20.0m away. The initial velocity of the ball is 10.0m/s and the building's height and the time it takes for the ball to reach the ground are unknown. The equation dv = Viv * t + 1/2a * t can be used to solve for these variables, but additional information is needed. The horizontal velocity is constant and can be used to determine the time of flight, while the vertical acceleration is -9.8m/s. Using the same equation, but with a = 0 for the horizontal direction, the correct answer can be obtained.

## Homework Statement

A ball is thrown horizontally from the top of a building and lands 20.0m away from it. If the ball is initially thrown at a velocity of 10.0m/s, how high is the building? How long does it take for the ball to reach the ground?

## Homework Equations

dv = Viv * t + 1/2a * t

## The Attempt at a Solution

dh (horiz.distance) = 20.0m
Vh = 10.0m/s
Viv (vertical init. velocity) = 0m/s
a = -9.8m/s
dv (vert. distance) = ?
t = ?

I'm confused because I'm missing two of the variables which are needed in the equation that will solve this problem...? (dv and t)

The horizontal velocity of the ball is fixed and constant during the whole time of flight. Knowing this, you can determine the time of flight.

Using the same equation as the one stated above? Because that one's giving me a totally wrong answer.

harujina said:
Using the same equation as the one stated above? Because that one's giving me a totally wrong answer.
Yes, the same equation, but of course in the horizontal direction a = 0. pls post your working.

I would first clarify the problem by stating that this is a horizontal projectile motion problem where the ball is thrown horizontally from the top of a building. I would also mention that the only force acting on the ball is gravity, which causes it to accelerate downwards at a rate of 9.8m/s^2.

To solve for the building height, we can use the equation dh = Vh * t, where dh is the horizontal distance, Vh is the initial horizontal velocity, and t is the time. In this case, we know dh and Vh, so we can rearrange the equation to solve for t. This gives us t = dh / Vh = 20.0m / 10.0m/s = 2.0s.

Now that we have the time, we can use the equation dv = Viv * t + 1/2a * t^2 to solve for the vertical distance. Here, dv is the vertical distance, Viv is the initial vertical velocity (which is 0 in this case), a is the acceleration due to gravity, and t is the time we just calculated. Plugging in the known values, we get dv = 0 * 2.0s + 1/2 (-9.8m/s^2) * (2.0s)^2 = -19.6m.

Since the vertical distance represents the height of the building, we can conclude that the building is 19.6m tall. To find the time it takes for the ball to reach the ground, we can use the equation dv = 1/2a * t^2 and solve for t. This gives us t = √(2 * dv / a) = √(2 * 19.6m / 9.8m/s^2) = √(4s^2) = 2.0s.

Therefore, it takes the ball 2.0 seconds to reach the ground. In summary, by using the equations for horizontal and vertical motion, we can solve for the building height and time in this horizontal projectile motion problem.

## What is horizontal projectile motion?

Horizontal projectile motion is the motion of an object that is launched horizontally and only affected by the force of gravity, resulting in a curved path called a projectile. This type of motion is also known as a constant velocity motion, where the object moves at a constant speed in the horizontal direction and a changing speed in the vertical direction due to the acceleration of gravity.

## What is the equation for horizontal projectile motion?

The equation for horizontal projectile motion is x = x0 + vxt, where x is the horizontal displacement, x0 is the initial horizontal position, vx is the initial horizontal velocity, and t is the time.

## What factors affect horizontal projectile motion?

The factors that affect horizontal projectile motion are the initial velocity, angle of launch, air resistance, and the acceleration of gravity. Any changes in these factors will result in changes in the horizontal displacement and the time of flight of the projectile.

## How is horizontal projectile motion different from vertical projectile motion?

Horizontal projectile motion is different from vertical projectile motion because it only involves motion in the horizontal direction, while vertical projectile motion involves motion in both the horizontal and vertical directions. Additionally, the acceleration due to gravity only affects the vertical motion in vertical projectile motion, while it affects both the horizontal and vertical motion in horizontal projectile motion.

## What is the range of a projectile?

The range of a projectile is the horizontal distance traveled by the object before it lands back on the ground. It can be calculated using the equation R = v02sin(2θ)/g, where R is the range, v0 is the initial velocity, θ is the angle of launch, and g is the acceleration of gravity. The maximum range is achieved when the angle of launch is 45 degrees.