Question in description

Question

Two softball players are practicing catching fly balls. One player throws a ball to the other. She throws the ball upward from a height of 5.5 feet with an initial vertical velocity of 40 feet per second for her teammate to catch.

a) Write an equation that models the height h (in feet) of the ball as a function of time t (in seconds) after it is thrown.

b) If her teammate misses the ball and it lands on the ground, how long was the ball in the air.

c) If her teammate catches the ball at a height of 5.5 feet, how long was the ball in the air? Explain your reasoning.

PLEASE HELP!!

Answer 1

(a) initial velocity is 40 ft/sec

intial height = 5.5 feet

Height function is:

h(t) = -16t^2 + (initial velocity) * t + (initial height)

where -16 is the gravity constant

h(t) = -16t^2 + 40t + 5.5

(b) 0 = -16t^2 + 40t + 5.5

0 = -160t^2 + 400t + 55

0 = 32t^2 -80t -11

quadratic formula says:

(80 +or- sqrt( 6400 + 4*32*11))/64

(80 +or- sqrt( 6400 + 1408))/64

(80 +or- sqrt(7808))/64

7808 = 4 * 1952 = 4 * 4* 488 = 4*4*4* 122 = 4*4*4*2*61

(80 +or- 8*sqrt(122))/64

(10 +or- sqrt(122))/8

negative branch disqualified as it results in negative measures

x = 2.631 approximately

(c) -16t^2 + 40t + 5.5 = 5.5

-16t^2 + 40t = 0

-8t ( 2t - 5) = 0

-8t=0 or 2t-5 = 0

t-0 or t = 5/2