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tokyokookie

Novice

Registered: 2023-08-25

Posts: 2

Solving Quadratics by Factoring and Graphing

Hello, I need help with these questions, thanks

18.   A tennis ball is launched straight upward with an initial velocity of 24.5 m/s from the edge of a cliff that is 117.6 meters above the ground. Which quadratic equation could be used to correctly determine when the ball will hit the ground:
4.9t2 + 24.5t + 117.6 = 0

-4.9t2 - 24.5t + 117.6 = 0

-4.9t2 + 24.5t - 117.6 = 0

4.9t2 + 24.5t - 117.6 = 0

-4.9t2 + 24.5t + 117.6 = 0

This is the one i chose: -4.9t² + 24.5t + 117.6   

19. Solve the equation you chose in question 18 to determine when the ball will hit the ground. (HINT: If you don't get one of the answers listed for this question, then maybe you chose the wrong equation in #18. Use this opportunity to double check your work!)

t = 8 seconds

t = 4 seconds

t = 3 seconds

t = -3 seconds

The ball will never reach the ground.

20. Using the same equation, determine when the ball is at a height of 49 meters.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Solving Quadratics by Factoring and Graphing

hi tokyokookie

Welcome to the forum.

With a question like this, you have to be careful about positive and negative.

Let's say we choose to make 'up'the positive direction. Then we have

s = - 117.6 because the ground is below the launch point.
u = + 24.5 as we are throwing upwards.
g = - 9.8 because  gravity make things go down.

So using s = ut + 0.5at^2

- 117.6 = 24.5t - 4.9t^2

rearranging

4.9t^2 - 24.5t - 117.6 = 0

That's ok as you can multiply mine by -1 to get yours.

x by 10 and divide by 7

7t^2 - 35t - 168 =0

divide by 7 again

t^2 - 5t - 24 = 0

(t-8)(t+3) = 0 so t = 8 or -3

In the context of the question -3 isn't an answer so choose t = 8.

In fact -3 does have some significance.  The ball obeys that equation even if we work backwards in time. If you start the ball on the ground at -3 seconds and let it zoom up, it will reach the clifftop at t = 0 and then carry on up for a while before coming back down at t = 8.

For part 20 just set s = 49. I haven't tried it yet but I'm expecting two answers; one when it's going up and another when it passes the same point on the way down.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

tokyokookie

Novice

Registered: 2023-08-25

Posts: 2

Re: Solving Quadratics by Factoring and Graphing

Thank you, I did it and got a 10