SOLUTION: The initial velocity of a rocket shot straight upward is 40 ft/sec. The height of the rocket after t seconds is given by the formula h(t) = -16t(squared) + 40 t. What is the maxim

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The initial velocity of a rocket shot straight upward is 40 ft/sec. The height of the rocket after t seconds is given by the formula h(t) = -16t(squared) + 40 t. What is the maxim      Log On


   

Question 426739: The initial velocity of a rocket shot straight upward is 40 ft/sec. The height of the rocket after t seconds is given by the formula h(t) = -16t(squared) + 40 t. What is the maximum height the rocket reaches? When will it land? Show and explain work.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h%28t%29+=+-16t%5E2+%2B+40t+
The maximum height occurs at
+t%5Bmax%5D+=+-b%2F%282a%29+ where
a+=+-16
b+=+40
+-b%2F%282a%29+=+-40%2F%282%2A-16%29+
+t%5Bmax%5D+=+5%2F4+
To find the max height,
+h%285%2F4%29+=+-16%2A%285%2F4%29%5E2+%2B+40%2A%285%2F4%29+
+h%285%2F4%29+=+-+25+%2B+50+
The max height is 25 ft
It will land when h+=+0
+0+=+-16t%5E2+%2B+40t+
+0+=+8t%2A%28-2t+%2B+5%29+
There are 2 ways for h(t) to be zero,
+8t+=+0+
+t+=+0+ ( at takeoff), and
+-2t+%2B+5+=+0
2t+=+5
+t+=+5%2F2+
The rocket will land in 2.5 sec
check answer:
+h%28t%29+=+-16t%5E2+%2B+40t+
+0+=+-16%2A2.5%5E2+%2B+40%2A2.5+
+0+=+-16%2A6.25+%2B+100+
+0+=+-100+%2B+100+
+0=+0+
OK
Here's a plot:
+graph%28+400%2C+400%2C+-1%2C+3%2C+-1%2C+30%2C+-16x%5E2+%2B+40x%29+