Algebra 1 7th Grade Gifted ; Quadratic Equations - Baseball Question

Question

In a baseball game, a pop fly is hit, and its height in meters relative to time in seconds is modeled by the function h(t)=4.9t^2+8t+1

a.) What direction does it open?

b.) For how many seconds is the ball in the air?

c.) When does the ball begin coming down after being hit?

d.) What is the maximum height of the baseball?

Answer 1

upward opening parabolic function

h= -4.9t^2 + 8t + 1

it hits the ground level when h = -4.9t^2 +8t + 1 = 0

t= 8/9.8 + (1/9.8)sqr(64 +4(4.9))

t = (8 + sqr(64+19.6)/9.8

t = about 1.75 seconds the ball is in the air

it starts coming down when it reaches maximum height, when h'(t) = -9.8t + 8 = 0. t= 8/9.8 = about 0.82 seconds

maximum height = h(0.82) = -4.9(8/9.8)^2 + 8(8/9.8) + 1 = -64/19.6 +6.53 +1= about 4.27 meters high

this all assumes there's a typo in the problem where it left out a minus sign before 4.9t^2

-4.9t^2 is the effect of gravity, 8 = initial velocity. 1= initial height