vertical motion

[Wren]

Parent trying to help my high schooler with Alg 1: please help with a step by step of HOW to do the problem. I am actually NOT asking for the answer but rather how to start and how to figure it out.
A baseball hit off the bat at 3 feet (initial height) with an initial velocity (v) of 132 ft/sec travels how long (time) before it hits the ground (since none of the players catches it)? We know how to set up the problem with the initial velocity and the initial height. What is the next step? What is the first H in H=-16t^2+132t+3? I sort of remember there is something to do when it is x^2 +x+y but I don't remember and I can't make heads or tails of her notes and it has me at sixes and sevens!

 

[Dr.Peterson]

We know how to set up the problem with the initial velocity and the initial height.

Do you mean that you wrote the equation, and are confident of it? (One question I'd have is whether the 132 ft/sec is meant to be the actual velocity at some angle, or the vertical component of velocity (or, unlike real baseball, it is hit straight up! But the equation you show is almost certainly what is intended, even if they stated the problem poorly.)

What is the first H in H=-16t^2+132t+3?

That would be the height of the ball at any time t>0.

What is the next step?

The goal is to find the time when the ball hits the ground; that would mean the first time that H = 0.

So replace H with 0 and solve the resulting equation, -16t^2+132t+3 = 0.

What methods have been taught for doing this? Do they know about the quadratic formula, or completing the square, or factoring?

Is there a textbook you can look at, with examples? Student notes may not always be clear, but there ought to be something.

 

[Dr.Peterson]

Looking for a good source for you, I gave your problem to Google, which said almost exactly what I said to start:

The question seems to be incomplete. Assuming the goal is to find the flight time with the given velocity as the initial vertical velocity component (or the ball was hit straight up), the solution is as follows:​

Then it proceeded to solve it completely, so we're glad you didn't do that yourselves!

Here is one site that may help:

Projectile Motion - MathBitsNotebook(A2)

Here's another:

Real World Examples of Quadratic Equations

Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.

www.mathsisfun.com