A ball is propelled upward from ground level After t seconds

A ball is propelled upward from ground level. After t seconds, its height in feet is defined by the equation: h(t) = -16t^2 + 128t with h(t) - height in feet and t = time in seconds Show work for all calculations and give concise explanations when necessary. a) What is the maximum height that the ball will reach and bow long will it take to reach maximum height (please include the appropriate units of measure)? b) Find h(5). Interpret these results is the ball on the way up or on the way down at this time? c) Find h(t) = 112. Interpret these results. Is the ball on the was up or on the way down at this time? d) Set up an equation and use algebra to show how to find out how many seconds will it take for the ball to hit the ground?

Solution

a . Given : h(t)= - 16 t²+128 t

= - 16 ( t² - 8t +16 -16 )

= - 16 [ t-4]² +256

First term is -ve Hence the maximu height reached = 256 and that happens when t=4

when t=4 ; h(t) = -16 x0 +256 =256 ft is the max ht and t=4

b. h(5) = -16 ( 5-4)²+256 = -16 +256= 240   

From part a we know that when t=4 the ball reaches the max ht hence when t=5 the ball is on the way down

c. h(t) =112 => -16(t-4)²+256 =112

=> 16(t-4)²= 144 , (t-4)² =9

=> t-4 = 3 , -3 or t= 7 , 1

when t =1 the ball is on the way up and whent=7 the ball is on the way down

d . To reach the top rom the ground level it takes 4 seconds to come back to ground another 4 secs

total the ball takes 8 secs to reach the ground