# Flight time and height

1. Sep 14, 2014

### jdawg

1. The problem statement, all variables and given/known data

A projectile is fired with an initial speed of 500 m/s at an angle of elevation of 45°. When and how far away will the projectile strike? How high overhead will the projectile be when it is 5 km downrange?

2. Relevant equations

3. The attempt at a solution
Flight time: t=$\frac{2(500)sin45°}{9.8}$
t=72.2 sec
How far: x=500cos45°(72.2)
x=25526.6 m

I'm not entirely sure how to figure out the second part though. I was thinking about using this formula: r(t)=vocosθ(t)+(vosinθ(t)-$\frac{1}{2}$gt2)
r(t)=x+(y-$\frac{1}{2}$gt2)
Am I on the right track with this? Do I use the t I calculated earlier for this equation?

Last edited: Sep 14, 2014
2. Sep 15, 2014

### haruspex

How long will it take to be that far down range?