SOLUTION: a ball is thrown vertically upward with an initial velocity of 128 feet per second. The distance in feet of the ball from the ground after t seconds is s=128t-16t^2. For what inter

Algebra ->  Rational-functions -> SOLUTION: a ball is thrown vertically upward with an initial velocity of 128 feet per second. The distance in feet of the ball from the ground after t seconds is s=128t-16t^2. For what inter      Log On


   

Question 732700: a ball is thrown vertically upward with an initial velocity of 128 feet per second. The distance in feet of the ball from the ground after t seconds is s=128t-16t^2. For what interval of time is the ball more than 240 above the ground?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There will be 2 solutions for +s+=+240+
You must solve for +t+ for both solutions
and then find +t%5B2%5D+-+t%5B1%5D+
+s+=+-16t%5E2+%2B+128t+
+240+=+-16t%5E2+%2B+128t+
+15+=+-t%5E2+%2B+8t+
+-t%5E2+%2B+8t+-+15+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-1+
+b+=+8+
+c+=+-15+
+t+=+%28-8+%2B-+sqrt%28+8%5E2+-+4%2A%28-1%29%2A%28-15%29+%29%29+%2F+%282%2A%28-1%29%29+
+t+=+%28-8+%2B-+sqrt%28+64+-+60+%29%29+%2F+%28-2%29+
+t+=+%28-8+%2B-+sqrt%28+4+%29%29+%2F+%28-2%29+
+t+=+%28-8+%2B+2%29+%2F+%28-2%29+
+t+=+3+
and
+t+=+%28-8+-+2%29+%2F+%28-2%29+
+t+=+5+
+5+-+3+=+2+
The interval of time the ball is more than 240 above the ground is 2 sec
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+10%2C+-30%2C+300%2C+-16x%5E2+%2B+128x+%29+