Formula for maximum height?

Question

Hi! On my physics homework it asks the maximum height of a ball thrown directly upward at 30m/s, ignoring air resistance and making acceleration 10m/s² downward. If this is all I know, what equation can I use to find the maximum height? My teacher's handwriting is largely illegible and I can't tell even nearly what it's supposed to be. Thank you!

Answer 1

Hi Fin,

Background:

Here are some general useful equations for motion that you are likely missing.

For motion with constant acceleration:

1. x = x₀ + v₀*t + 1/2a*t²
2. v = v₀ + a*t
3. v² = v₀² + 2a(Δx)

Since you are dealing with free-fall the ball would typically be accelerating downward due to gravity. In other words, a = -g = -9.81m/s², but you are told to assume a = -10 m/s² for this problem.

Now, take your pencil and throw it into the air a couple times. You should notice that when your pencil is at its peak high the velocity is zero! This is an extremely important characteristic that allows us to solve this problem.

Solving your question:

Initially we are told that

v₀ = 30 m/s

a = -10 m/s²

and we know that

v(max height) = 0

Using equation 2 we can solve the amount of time it takes to reach the maximum height:

v = v₀ + a*t

0 = 30 - 10*t

t = 3 sec

Now we need to solve for the maximum height using equation 1. (I'm going to assume x₀ = 0 m since it was not defined.)

x = x₀ + v₀*t + 1/2a*t²

x_max = 0 + 30*3 - 1/2*10*3^2 = 90 - 90/2 = 45 m

I hope that helps! I also suggest googling "AP Physics Equation sheet". I found this to be the most comprehensive list of equations you will use during Physics.

Good luck,

Bryce