Math word problem (John is tossing a baseball)

Question

John is tossing a baseball into the air. When he throws the ball, his hand is 8 feet above the ground, and the initial speed of the ball is 64ft/sec. what is the maximum height of the ball? About how long will it take the ball to strlike johns glove if he catches it at a height of 6 feet? The height of the baseball is given the equation below, where t is in seconds. Round to the nearest height and second. H(t)=—16t^2+64t+8

Answer 1

take the derivative and set it equal to zero, solve for t, then subsitute that t value into the original H(t) equation to solve for maximum height

-32t +64 = 0, t = 2 seconds H(2) = -16(2)^2 +64(2)+8 = 72 feet = max height

H(t) = 6 = -16t^2 + 64t + 8

-16t^2 + 64t +2 = 0

8t^2 -32t -1 = 0

t = 32/16 + (1/16)sqr(32^2 +32) = 2+2.03 = 4.03 seconds when he catches it at 6 feet, about 4 seconds