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## Homework Statement

A student throws a set of keys vertically upward to his fraternity brother, who is in a window a distance

*h*above. The brother's outstretched hands catches the keys on their way up at a time

*t*later. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught? (

*Answer should be in terms of h, t, and g.*)

## Homework Equations

[itex]\Delta[/itex]x = v

_{0}t + (1/2)at

^{2}

v

^{2}= v

_{0}

^{2}+ 2a[itex]\Delta[/itex]x

## The Attempt at a Solution

Question 1: when did the act of throwing begin? When the keys were released from the hand, or during the wind up of the arm/hand, before releasing the keys? The physics tutor in the math lab told me the initial velocity was 0. But that is not true if at the moment of release the keys were already at a higher velocity.

Question 2: what does "[a]nswer should be in terms of

*h*,

*t*, and

*g*" mean? Do they want actual numbers using h, t, and g; or is this a numberless problem?

a) [itex]\Delta[/itex]x = v

_{0}t + (1/2)at

^{2}

v

_{0}= (1/t)([itex]\Delta[/itex]x - (1/2)at

^{2})

v

_{0}= (1/t)(h - (1/2)gt

^{2})

v

_{0}= (h/t) - ((gt)/2)

b) v

^{2}= v

_{0}

^{2}+ 2a[itex]\Delta[/itex]x

v

^{2}= ((h/t) - (gt)/2)

^{2}+ 2gh

v = +(h/t) - (gt)/2 + 2gh

*and*v = -((h/t) - (gt)/2 + 2gh)

Since they keys were thrown upward and caught,

*v*in this case must be the positive answer above.

Thanks for any help!

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