# Velocity Problems In Calculus

[mage lang=”” source=”flickr”]velocity problems in calculus[/mage]

**Velocity problem in calculus?**

I’m doing calculus 2, and this problem is asking for the Vo. Can i have some help lease.

What must the initial velocity of a bullet fired vertically be to reach a height of 1600 feet?

we will assume we are on earth

the acceleration (deceleration) due to gravity is 32 feet per second squared

integrating 32: (acceleration

the velocity is 32t + c feet per second where t = time in seconds

integrating 32t + c to get position

32t^2/2 +ct +d (position equation)

so, for this problem I find that it is much easier to look at an equivalent and opposite problem, where the bullet is dropped from 1600 feet. This eliminates solving for constants.

from the position equation, 16t^2 = 1600

t^2= 100

t = 10

so not, substituting back into the velocity equation, we will find the velocity after 10 seconds of acceleration at 32 feet per second squared:

v = 32*t

v = 32*10

v= 320 feet per second

I hope this helps.

**I Will Derive!**