# Projectile Puzzle

1. Sep 19, 2008

### robvba

Two balls are thrown in the air at different angles, but each reaches the same height. Which ball remains in the air longer?

a the one thrown at the steeper angle
b the one thrown at a shallower angle
c both remain in the air the same time

I'm thinking that V must be greater for the lower angle ball. And V = V0 for both.
At first i thought that the time that an object spends in the air is proportional to its height.
However, i'm confused because using t=V0/g results in a greater t for the faster projectile.

2. Sep 19, 2008

### Kurdt

Staff Emeritus
Think about the vertical component of each balls velocity. What must they be if the balls reach the same height?

3. Sep 19, 2008

### robvba

Using Y-Y0=Vy0t-1/2gt^2 for the vertical component, and considering that Vy0 will be different for both while the height is fixed, than the one with the greather Vy0 will spend more time in the air. However, given that the only vertical force acting on an object is gravity, they must spend the same amount of time in the air...?

4. Sep 19, 2008

### Kurdt

Staff Emeritus
Yes both balls must have the same vertical component of velocity. If that is true they must both spend the same time in the air.

5. Sep 19, 2008

### robvba

Ok. So the speed and angle would result in a vertical velocity component that would be equivalent between the two. Thanks you