# Time at which a projectile reaches a certain height

• enantiomer1
In summary, the conversation discusses a physics question about a baseball being hit at a certain speed and angle. The question asks for the two times when the ball is at a height of 10.0 m. Different methods are suggested, such as trial and error or using the quadratic formula, to solve for the time values. The conversation ends with a suggestion to find the maximum height and use that to calculate the two times.
enantiomer1

## Homework Statement

Hey, I think I understand this question but there's one or two parts that are really confusing me, the question is:
A major leaguer hits a baseball so that it leaves the bat at a speed of 31.0 m/s and at an angle of 36.1 degrees above the horizontal. You can ignore air resistance.
At what two times is the baseball at a height of 10.0 m above the point at which it left the bat?

## Homework Equations

I realize that the equation I should be using is:
y=(v0sin)*t- 1/2*g*t2

## The Attempt at a Solution

so far I've tried various things but I fee like I'm missing something cause I can't figure out how to get t, is there some variabe or function for t that I can substitute in order to get the equation?

You could do it by trial and error - put in various times and see when y = 10.
Graph the whole thing on a calculator and trace until you find points with y = 10.

When you replace y with 10, you will have a quadratic equation which can be solved in various ways - notably the quadratic formula.

that's nice and all, but it isn't going to help me on the test

find out it's maximum height and the time it reaches it. from there you can add or subract time to find when it's 10m high

enantiomer1 said:
that's nice and all, but it isn't going to help me on the test

Im pretty sure what delphi said WILL help you on the test and is the best way to go about the problem.

you were given a y-function and you know that you are looking for a height of 10m. You know the angle, Vo and g. As delphi said, that gives you a quadratic. You solve the quadratic formula for values of t when the ball is 10 meters high. You'll get two values for that...

## 1. What is the formula for calculating the time at which a projectile reaches a certain height?

The formula for calculating the time at which a projectile reaches a certain height is t = √(2h/g), where t is the time in seconds, h is the height in meters, and g is the acceleration due to gravity (9.8 m/s²).

## 2. Does the weight of the projectile affect the time it takes to reach a certain height?

No, the weight of the projectile does not affect the time it takes to reach a certain height. The time is solely determined by the initial velocity and the height of the projectile.

## 3. How does air resistance impact the time at which a projectile reaches a certain height?

Air resistance can slightly affect the time at which a projectile reaches a certain height, as it can slow down the projectile's motion and cause it to take slightly longer to reach the desired height.

## 4. Can the angle of launch affect the time at which a projectile reaches a certain height?

Yes, the angle of launch can affect the time at which a projectile reaches a certain height. A steeper angle will result in a longer flight time and a higher final height, while a shallower angle will result in a shorter flight time and a lower final height.

## 5. How can we use the time at which a projectile reaches a certain height in real-life applications?

The time at which a projectile reaches a certain height can be used in various real-life applications, such as calculating the flight time of a rocket or the hang time of a basketball. It is also useful in determining the optimal angle of launch for a projectile to reach a certain height.

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