Question

please help!! A baseball is thrown upward from ground
level with an initial velocity of 49 feet per
second, and its height h in feet is given by
h = −16t^2 + 49t, 0 < or equal to t < or equal to 3
where t is the time in seconds. Suppose you
are told that the ball reaches a height of 64
feet. Is this possible?
1. No
2. It cannot be determined.
3. Yes

Answer 1

find the max of this parabola.

Answer 2

in place of h plug 64..
and find the discriminant of the resulting quadratc..

Answer 3

so i solve for t?

Answer 4

yup dear...
without solving also u can answer just by finding the dicriminant of the quadratic..

Answer 5

how do i find the discriminant of the quadratic

Answer 6

for the quadratic ax^2 +bx+c=0 the discriminant is given by b^2 - 4ac

Answer 7

if b^2 - 4ac < 0 then it is not possible other wise its possible..

Answer 8

so it'll be -16x^2+49+c?

Answer 9

it will be 16t^2 - 49t +64 =0

Answer 10

and I will solve for t?

Answer 11

yup..

Answer 12

wouldn't it be-16t^2

Answer 13

is it 2? cannot be determined?

Answer 14

after
adjusting the terms...(u can do even with the term-16t^2

Answer 15

is it 2?

Answer 16

3

Answer 17

can you show me how?

Answer 18

find t using quadratic formula..

Answer 19

its not 3 i checked and it said it was wrong

Answer 20

after finding t u need to check the domain condition..

Answer 21

can you help lovely soilder?

Answer 22

let me ask you a question? can you picture the path of the ball being thrown upward?

Answer 23

yes

Answer 24

ok...that's always step one. if you can picture the problem, then you are half way there...

so you can see that the ball will reach a maximum height and then start to come down.

the question is, "will the ball reach a height of 64 feet before it comes down?"

Answer 25

okay

Answer 26

what matricked was saying is that you don't really need to find t to solve this, you just need to know if there *is* a t that will solve it.

that's a nuch easier problem to answer.

Answer 27

if there *is* a t, then the equation
\[-16t^{2} + 49t = 64\] has a solution

Answer 28

move the 64 to the other side (since we like quadratics equal to zero) and you have
\[-16t^{2} + 49t - 64 = 0\]

whether or not this has a solution can be found using the disrciminate.

Answer 29

next question for you...do you know the quadratic formula?

Answer 30

i know of it , but i forgot how it went

Answer 31

fair enough...normally we would solve a quadratic using the formula
\[t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\]

but we don't care about the value of t...only if it exists.

that formula will have a solution as long as we don't try to take the sqrt of a negative number (which is a no-no in the real world)

so the \[b^{2}-4ac\] part is called the discriminate.

Answer 32

calculate that...if it is negative, then the answer to the question is "no" if it is zero or positive, the answer is "yes"...

Answer 33

it's actually -64 because you set the original formula = 64 which became -64 when you move it to the other side...

Answer 34

i got a negative

Answer 35

@mtbender74

Answer 36

i also get a negative...so what does that tell you?

Answer 37

no?

Answer 38

that tells you that the ball never reaches a height of 64 feet off the ground. :) so...the answer to your question is "No"

Answer 39

thank you!!

Answer 40

makes sense?

Answer 41

yes a lot

Answer 42

good :)