Question

A batter hits a baseball upward with an initial speed of 96 feet per second. After how many seconds does the ball hit the ground? Use the formula h = rt − 16t2 where h represents height in feet and r represents the initial speed.

Answer 1

Well, what values should we use for h and r?

Answer 2

Um, im not sure

Answer 3

h is the height above the ground. we need to find t when the ball hits the ground. What should h be equal to ?

Answer 4

0 ? i dont know

Answer 5

Yes, because the ball starts from ground level and ends up there too.

Answer 6

What about r? That's the speed of the ball.

Answer 7

96

Answer 8

Correct. Notice that r > 0 and the coefficient of t^2 is < 0. That's because the ball starts out going up, and gravity accelerates downward. Now all you have to do is solve
-16t^2 + 96t = 0

Answer 9

Why not multiply both sides by 1/16 to start with?

Answer 10

okay

Answer 11

-t^2 + 6t = 0

Answer 12

Now, one solution to this is 0. That's the solution when the ball is just starting up. If we multiply both sides by 1/t that's OK in this case. What do you get?

Answer 13

i dont understand that part ?

Answer 14

(1/t) (-t^2 + 6t) = (1/t) 0 = 0
-t + 6 = 0

Answer 15

Do you understand that?

Answer 16

yeah

Answer 17

t = 6

Answer 18

Now, plug 6 back into the original equation to make sure it's correct, and you're done.

Answer 19

thank you

Answer 20

yw

Answer 21

sorry, posted to the wrong thread, but I hope you are happy with what we did

Answer 22

you are very welcome