Question

A ball is thrown from an initial height of 3 meters with an initial upward velocity of 9 m/s. The ball's helght h (in meters) after 1 seconds is given

by the following
h=3+9t-5t^2
Find all values of t for which the ball's height is 6 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)

Answer 1

Answer:t = 0.268 seconds

t= 3.32 seconds

Find all values of t for which the ball's height is 8 meters.

h = -5t2 + 20t + 3

8 = -5t2 + 20t + 3

Subtract 8 from both sides of the equation

0 = -5t2 + 20t - 5

This is a parabola which opens downward

a = -5

b = 20

c = -5

the vertex -b/2a, h; (2, 23)

-20/2(-5) = -20/-10 = 2

h = -5(22) + 20(2) + 3

h = -20 + 40 + 3 = 23

Use the Quadratic Formula to solve for t

0 = -5t2 + 20t - 5

Dividing both sides of the equation by 5 makes the math easier

0 = -t2 + 4t -1

Now

a = -1

b = 4

c = 1

(-b±(√b2-4ac))/2a

(-4(±√16 - 4))/-2

(-4±(√12))/-2

-4/-2 + 2√3/-2

2 - √3 = 0.26795 seconds

-4/-2 - 2√3/-2

2 + √3 = 3.732 seconds

Explanation: