Help with word problem

Question

An object is launched from a window ledge on a tall building. The height of the object above the ground can be found using the function h(t) = -49/10 t² + 196/10 t + 588/10 where t stands for the number of seconds and h is the height in meters

question1 : find the height of the window ledge (write number only in decimal form )

question 2:when does the object reach its maximum height ?(number only)

question 3 : write an equation you could use to find how long it takes the object to reach the ground . ( write each number in the equation in decimal form)

Answer 1

Question 1 = the height of the window ledge is the height of the object when t = 0, or the y-intercept. From the equation you can tell that this is 58.8

Question 2 = Maximum height can be found by graphing the function and finding the vertex. This occurs at the point (2, 78.4) This means the maximum height occurs after 2 seconds

Question 3 = You want to set the height equation equal to zero which would look like this:

-4.9t² + 19.6t + 58.8 = 0

Answer 2

(a) t=0 ---> 588/10 = 68.8

(b) A = -49/10 B = 196/10 C = 588/10

max occurs at -B/(2a) = 196/10 / [ 2 * -49/10]

= 196/10 / [-98/10]

= 196/10 * 10/-98

= 196/-98

= -2

the max height is -49/10(-2)^2 + 196/10(-2) + 588/10

= -49/10(4) + 196/10(-2) + 588/10

= -196/40 + -392/20 + 588/10

= -196/40 + -386/40 + 2352/40

= (-196+-386+2352)/40

= 1770/40

= 177/4

= 44.25 = 44 and 1/4

(c) -49/10 t^2 + 196/10t +588/10 = 0

49t^2 - 196t - 588 = 0 <-- multiplies by -10

49 (t^2 - 4t - 12) =0

(t - 6)(t+2)=0

t=6 or t=-2

6 seconds