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After t sec. a ball tossed in the air from ground level reaches a height of h feet given by the equation: h=144t-16t^2

a. what is the height of the ball after 3 sec.? 288 ft.

b. what is the maximum height the ball will reach

c. find the number of seconds the ball is in the air when it reaches 224 ft in height

d. after how many sec. will the ball hit the ground before rebound?



I am not sure which equation to use and why for the b,c,and d. If I find the ft/sec. that the ball travels (96), and set the quadratic equation to -16t^2+144t+288 or 16t^2-144t-288=0, is this correct? Or should I use the quad formula and why.



Answer :

mathdragon
Don't modify the equation. It is true that f(3)= 288 for f(t) = -16t^2 +144t

the maximum height of the ball will be where the derivative is zero. In other words you could find the height of the ball by converting this into vertex form, or you could find it by calculating the time needed for the ball to reach its maximum height.

0=-32t+144

t=3 till max and max is 288

224=-16t^2 +144t
0= -16t^2+144t-224

t=2 but then the ball will reach 224 ft again at t=7

the ball reaches its maximum height at t=3 seconds and a parabola is symmetric, so at t=6 seconds it will contact the ground again.


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