# How long does it take a football to reach max height?

## Homework Statement

how long does it take a football, with an initial velocity of 30 m/s at 30 degrees up from the horizontal, to reach the top of its flight?

## Homework Equations

Δy= ½ (Vf + Vo) t

## The Attempt at a Solution

I know that Vf= 0 m/s here because when it reaches the highest point, it stops for a split second. I also know that the horizontal component is 30sin(30), which equals 15. I then plugged it into the equation above to get

15= ½ (0+30)t → 15= 15t → t= 1 second.
Is this process correct?

I know that Vf= 0 m/s here because when it reaches the highest point, it stops for a split second

Yes, in the vertical direction the ball's velocity will be zero at some instant.

I also know that the horizontal component is 30sin(30), which equals 15

You mean 'vertical,' right?

Δy= ½ (Vf + Vo) t
15= ½ (0+30)t → 15= 15t → t= 1 second.

I see two unknowns in this equation. You have plugged in a speed for a displacement. If you want to use that particular equation to find time you'll first need to find the vertical displacement. There is, however, another way to do it. What do you think?

Yes, in the vertical direction the ball's velocity will be zero at some instant.

You mean 'vertical,' right?

I see two unknowns in this equation. You have plugged in a speed for a displacement. If you want to use that particular equation to find time you'll first need to find the vertical displacement. There is, however, another way to do it. What do you think?

okay I see my mistakes, and yes I did mean vertical, thank you. Could I do change in vertical velocity (which is 0-15m/s) = acceleration in the y direction times time to figure it out? so -15 = -9.8 (t) -----> so time = 1.53 seconds?

Looks good.