The muzzle velocity of a cannon is 480 feet per second. if a cannonbal is fired vertically, at whattimes will it be at a height of 3,344

Question

The muzzle velocity of a cannon is 480 feet per second. if a cannonball is fired vertically, at what times will it be at a height of 3,344?

Answer 1

The height h(t) as a function of time t is given by

 

h(t) = -(1/2)gt² + v_ot + h₀

 

where

 

g = acceleration of gravity = 32 ft/s²

v₀ = vertical component of muzzle velocity = 480 ft/s

h₀ = 0 if fired from the ground

 

Then

 

h(t) = -16t² + 480t

 

Set h(t) = 3344 ft and solve for t.

 

3344 = -16t² + 480t

 

-16t² + 480t - 3344 = 0

 

t² - 30t + 209 = 0

 

t = 11 and 19 seconds

 

It reaches 3344 ft in 11 seconds on the way up, and again in 19 seconds on the way down.