# At which times will the ball be at a height of 15 meters?

• Gdsykes
In summary, the problem is to find the times at which a ball thrown upward with a velocity of +20m/sec on a planet with an acceleration due to gravity of -10m/sec² will reach a height of 15 meters. The equations used are D=ViT+½at² and t-v+- v²+f(1/2a)d (square root) / 2(1/2a), and the quadratic formula is used to solve for time when D = 15m.
Gdsykes

## Homework Statement

I am in high school physics. This is my problem that I've been trying to work on: A ball is thrown straight upward with a velocity of +20m/sec on a planet where the acceleration due to gravity is -10m/sec². Find the times at which the ball will be at a height of 15 meters.

## Homework Equations

Ok, so I started with this equation: D=ViT+½at². I'm not sure if it's the correct one to use, but I'm pretty sure it is...I think I will need to use the quadratic forumla: x= -b+-b²-4ac (square root)/2a. Sorry, I don't know how to make a square root symbol or any of the other signs?!?

## The Attempt at a Solution

Now, the problem calls for time, so I must need to solve for it. Next, I got this as the possible equation to utilize when it's solved for time: t-v+- v²+f(1/2a)d (square root) / 2(1/2a)
So far, does everything seem to be right, now all I need to do is "plug and chug?" :) Thanks
-Greg

Just take you equation for D and use the quadratic formula (or some other method) to solve for t when D = 15m. (Note that at t = 0, D = 0)

S=ut + 1/2 at^2
it should be used in a straight line motion and uniform acceleration.

## 1. What factors affect the height of a ball?

The height of a ball is primarily affected by the initial velocity at which it is thrown or launched, the force of gravity, and air resistance. Other factors that may also play a role include the shape and weight of the ball, the angle at which it is thrown, and any external forces acting upon it.

## 2. How can I calculate the time at which the ball will reach a specific height?

To calculate the time at which the ball will reach a specific height, you can use the equation h(t) = h0 + v0t - 1/2gt2, where h(t) is the height at time t, h0 is the initial height, v0 is the initial velocity, and g is the acceleration due to gravity. Rearranging the equation to solve for t will give you the time at which the ball reaches the desired height.

## 3. What is the maximum height a ball can reach?

The maximum height a ball can reach is dependent on the initial velocity and angle at which it is thrown, as well as the force of gravity and air resistance. In a vacuum, a ball with an initial velocity v0 will reach a maximum height of hmax = v02/2g. However, in real-world situations, air resistance will cause the ball to reach a lower maximum height.

## 4. Can a ball reach a height of 15 meters multiple times?

Yes, a ball can reach a height of 15 meters multiple times if it is thrown or launched with enough initial velocity. However, the time at which it reaches this height may vary depending on the factors mentioned in the first question. Additionally, air resistance may cause the ball to reach a slightly different height each time.

## 5. How does the height of a ball change over time?

The height of a ball changes over time due to the force of gravity and air resistance. Initially, the ball will have an upward trajectory as it gains height, but eventually, the force of gravity will cause it to decelerate and begin falling back towards the ground. The height of the ball will continue to decrease until it reaches the ground or comes into contact with another surface.

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