falling object question: A rock is thrown vertically upwards

[dbob85]

A rock is thrown vertically upwards from the edge of a cliff. It's height in feet measured above the ground at the base of the cliff, t seconds later, is given by the expression: y(t) = -16t^2 + 56t + 32

1) Compute the velocity of the rock using V(t) = lim [u->t] y(u)-y(t)/u-t

But wouldn't that equation equal 0?

2) When does the ball hit the ground, and what is the impact velocity at that instant?

3)When does the rock have a velocity of 0, and what happens to the rock at that instant?

Is the rock at its highest point when the velocity is zero? And is the answer to the last part of this that the rock begins to fall?

 

[dbob85]

is there anyone who can help?

 

[stapel]

is there anyone who can help?

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A rock is thrown vertically upwards from the edge of a cliff. It's height in feet measured above the ground at the base of the cliff, t seconds later, is given by the expression: y(t) = -16t^2 + 56t + 32
1) Compute the velocity of the rock using V(t)= lim u->t y(u)-y(t)/u-t

I will assume this means [(y(u) - y(t)] / [u - t].

Plug "u" into y(t).

Subtract y(t) (the expression) from y(u). Simplify. You should get:

. . . . .-16[(u - t)(u + t)] + 56[u - t] = [u - t][-16(u + t) + 56]

Divide the simplified difference by "u - t". Cancel off the common factor.

Take the limit at u approaches t.

2) When does the ball hit the ground and what is the impact velocity at that instant?

At what point (value of t) is y(t) equal to zero?

What is value of the velocity expression (from part (1) above) at this value of t?

3) When does the rock have a velocity of 0? and what happens to the rock at that instant?

Think about what happens to the speed of an object after it is thrown upward. It ends up eventually on the ground. How does it get there? How does its speed change on the way?

Eliz.

 

[dbob85]

how do you plug u in for t?sorry about the rude comment i'm just learning how to use this

 

[stapel]

how do you plug u in for t?

Working with function notation and variables should have been covered extensively back in algebra, long before this stage.

To plug something in for a variable, you take every instance of the variable, and replace the variable with that something. For instance:

. . . . .f(x) = 3x + 4

Then:

. . . . .f(2) = 3(2) + 4

. . . . .f(-12) = 3(-12) + 4

. . . . .f(t) = 3(t) + 4

. . . . .f(4y) = 3(4y) + 4

. . . . .f(s²) = 3(s²) + 4

And so forth. If this is utterly unfamiliar, then I would suggest having a serious talk with your academic advisor, because it would appear that you have been placed in a course for which they have not provided you with the necessary background material.

Eliz.

 

[dbob85]

okay one last question how do you take the limit as (u) goes to (t)

 

[stapel]

okay one last question how do you take the limit as (u) goes to (t)

The concepts and processes related to limits should have taken at least one entire chapter of your book, and perhaps a month of class time. I'm afraid we simply cannot replicate that instruction here, certainly not in any "fifty words or less" version that would fit in a forum posting.

It sounds like many foundational concepts have not been covered during your previous courses. Please have a serious heart-to-heart with your academic advisor regarding course placement, so you can get this necessary background material.

Good luck!

Eliz.