SOLUTION: A cannon ball is fired from a cliff that is 260 feet high with an initial speed of 128 feet per second. The height H of the cannon ball in feet as a function of time in seconds can

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Question 1005220: A cannon ball is fired from a cliff that is 260 feet high with an initial speed of 128 feet per second. The height H of the cannon ball in feet as a function of time in seconds can be modeled by the function h(t)= -16t^2 + 64t +260
a. When will the height of the cannon ball be 320 feet?
b.what is the time of flight?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h%28t%29=+-16t%5E2+%2B+64t+%2B260+
(a)
+h%28t%29+=+320+
+320+=+-16t%5E2+%2B+64t+%2B260+
+-16t%5E2+%2B+64t+-+60+=+0+
+-4t%5E2+%2B+16t+-+15+=+0+
use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-4+
+b+=+16+
+c+=+-15+
+t+=+%28+-16+%2B-+sqrt%28+16%5E2+-+4%2A%28-4%29%2A%28-15%29+%29%29+%2F+%282%2A%28-4%29%29+
+t+=+%28+-16+%2B-+sqrt%28+256+-+240+%29%29+%2F+%28-8+%29+
+t+=+%28+-16+%2B-+sqrt%28+16+%29+%29+%2F+%28-8%29+
+t+=+%28+-16+%2B+4+%29+%2F+%28-8%29+
+t+=+3%2F2+
and, also:
+t+=+%28+-16+-+4+%29+%2F+%28-8%29+
+t+=+5%2F2+
------------
The height will be 320 ft at t = 3/2 sec ( on the way up )
and t = 5/2 sec ( on the way down )
------------------------------
The time of flight ends when +h%28t%29+=+0+ again
+h%28t%29+=+-16t%5E2+%2B+64t+%2B260+
+0+=+-16t%5E2+%2B+64t+%2B260+
+-4t%5E2+%2B+16t+%2B+65+=+0+
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-4+
+b+=+16+
+c+=+65+
+t+=+%28+-16+%2B-+sqrt%28+16%5E2+-+4%2A%28-4%29%2A65+%29%29+%2F+%282%2A%28-4%29%29+
+t+=+%28+-16+%2B-+sqrt%28+256+%2B+1040+%29%29+%2F+%28-8+%29+
+t+=+%28+-16+%2B-+sqrt%28+1296+%29%29+%2F+%28-8+%29+
+t+=+%28+-16+%2B+36+%29+%2F+%28-8+%29+ ( this gives negative time -can't use )
+t+=+%28+-16+-+36+%29+%2F+%28-8+%29+
+t+=+52%2F8+
+t+=+6.5+
The flight is over in 6.5 sec
-------------------------
Here's a plot of the flight:
+graph%28+500%2C+500%2C+-1%2C+8%2C+-50%2C+360%2C+-16x%5E2+%2B+64x+%2B+260+%29+
( I figured out that the maximum height is 324 ft )