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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Levi (Customer)

[00:00:00] In a football game, a defensive player jumps up to block a pass by the opposing team's quarterback. The player bats the ball downward with his hand at an initial vertical velocity of -51 ft/sec when the ball is 7 ft above the ground. How long do the defensive player's teammates have to intercept the ball before it hits the ground? The model for an object that is launched is on the whiteboard. The topic for the lesson is the quadratic formula.

Jon J (Tutor)

[00:00:08] Hello, welcome to tutor.com !

Levi (Customer)

[00:00:14] Hi, thanks.

Jon J (Tutor)

[00:00:18] Have you started to work on this problem yet?

Levi (Customer)

[00:00:44] No, I'm not sure what the
variables stand for or what to
plug in.

Jon J (Tutor)

[00:01:02] okay, first let's look at what the variables stand for

[00:01:20] If you were to take a guess, what do you think h0 stands for?

Levi (Customer)

[00:01:37] the original height?

[00:01:43] ie height when time = 0?

Jon J (Tutor)

[00:01:46] Perfect! That is right

[00:01:55] What would you guess for V0?

Levi (Customer)

[00:02:09] vertical velocity, so -50?

Jon J (Tutor)

[00:02:28] Good, you've got the right idea

[00:02:50] It looks like in the problem the starting velocity is -51

Levi (Customer)

[00:03:07] That's a typo on my part,
sorry.

Jon J (Tutor)

[00:03:09] Next we just need to plug in those values

Levi (Customer)

[00:03:15] It's actually -50 ft/sec

Jon J (Tutor)

[00:03:51] Now what do you think we should do?

Levi (Customer)

[00:04:07] And this implying h(t) = 0? At
this point my instincts say to
apply the quadratic formula.

Jon J (Tutor)

[00:04:14] you got it!

[00:04:29] Why does setting it equal to zero make sense in this situation?

Levi (Customer)

[00:05:01] Because you want to know
how long it takes for the ball
to be at zero feet, on the
ground.

Jon J (Tutor)

[00:05:13] Very nice explanation

Levi (Customer)

[00:06:44] That's an awfully big radical.

Jon J (Tutor)

[00:06:53] good, now all that this left is to solve it

[00:07:12] In the end, we should get relatively small numbers

Levi (Customer)

[00:07:24] 737 and 4 will both work here.

Jon J (Tutor)

[00:08:52] Are you allowed to use calculators at all, or are you asked to leave the answer in fraction form?

Levi (Customer)

[00:09:12] calculators are allowed to
simplify down as far as we can.

Jon J (Tutor)

[00:09:19] okay

[00:09:45] So, what you have appears to almost as simple as we can make it

[00:10:02] We can do a bit of work on the fractions

[00:10:29] Good! Next we should ask ourselves if both solutions work

[00:10:38] And if not, which is the true answer?

[00:11:29] Because we now have these two options

Levi (Customer)

[00:11:40] What about the negative on
the 16?

Jon J (Tutor)

[00:12:13] in one of the solutions, subtracting a negative can be rewritten as addition

Levi (Customer)

[00:12:36] Then adding a negative could
be considered subtraction...
okay, I think I get it.

[00:12:52] Having a negative time makes
no sense.

Jon J (Tutor)

[00:12:58] You got it!

[00:13:06] So the first one can't be a solution

[00:13:15] And the second must be what we need

[00:13:58] I found that comes out to approximately 0.134 seconds, which also seems like a reasonable amount of time for it to fall 7 feet

[00:14:11] Do you have any questions about anything we went over today?

Levi (Customer)

[00:14:23] Nope, this was perfect, thank
you.

Jon J (Tutor)

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