SOLUTION: To avoid a sand trap, a golfer hits a ball so that its height is represented by equation h = -16t^2 + 80t, where h is height measured in feet and t is the time measured in seconds.

Algebra ->  Functions -> SOLUTION: To avoid a sand trap, a golfer hits a ball so that its height is represented by equation h = -16t^2 + 80t, where h is height measured in feet and t is the time measured in seconds.      Log On


   

Question 1076210: To avoid a sand trap, a golfer hits a ball so that its height is represented by equation h = -16t^2 + 80t, where h is height measured in feet and t is the time measured in seconds.
a. when does the ball land on the ground?
b. what is maximum height of the ball during its flight?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h+=+-16t%5E2+%2B+80t+
(a)
The ball is on the ground ( h = 0 ) at 2 times
(1) instant the ball is hit ( t = 0 )
(2) instant the ball returns to ground
------------------------------------------
Set the height equal to zero
+0+=+-16t%5E2+%2B+80t+
+t%2A%28+-16t+%2B+80+%29+=+0+
+-16t+%2B+80+=+0+
+16t+=+80+
+t+=+5+
The ball hits the ground in 5 sec
-------------------------------
(b)
The t-value of the maximum height is given
by the formula:
+t%5Bmax%5D+=+-b%2F%282a%29+
when the equation looks like:
+h+=+a%2At%5E2+%2B+b%2At+%2B+c+ ( note that c=0 )
+a+=+-16+
+b+=+80+
+t%5Bmax%5D+=+-80%2F%282%28-16%29%29+
+t%5Bmax%5D+=+80%2F32+
+t%5Bmax%5D+=+2.5+ sec
Plug this result back into equation
+h%5Bmax%5D+=+-16t%5E2+%2B+80t+
+h%5Bmax%5D+=+-16%2A2.5%5E2+%2B+80%2A2.5+
+h%5Bmax%5D+=+-16%2A6.25+%2B+200+
+h%5Bmax%5D+=+-100+%2B+200+
+h%5Bmax%5D+=+100+
The maximum height is 100 ft
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Here's the graph:
+graph%28+400%2C+400%2C+-1%2C+6%2C+-10%2C+120%2C+-16x%5E2+%2B+80x+%29+