PROBLEM $1$

You drop a $2\mathrm{.}00kg$ book to a friend who stands on the ground at distance $D=10\mathrm{.}0m$ below. If your friend's outstretched hands are at distance $d=1\mathrm{.}50m$ above the ground.

$($a$)$ What is the speed of the book when it reaches the hand:

$($b$)$ If we substituted a second book with twice the mass, what would its speed be$?$

$($c$)$ If$,$ instead, the book were thrown down, would the answer to $($a$)$ increase, decrease, or remain the same?

PROBLEM $2$

Figure here shows a ball with mass $m=0\mathrm{.}341kg$ attached to the end of a thin rod with length $L=0\mathrm{.}452m$ and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle.

The rod is held horizontally as shown and then given enough of a downward push to cause the ball to swing down and around and just reach the vertically up position, with zero speed there.

$($a$)$ What initial speed must be given the ball so that it reaches the vertically upward position with zero speed?

Mass $m=0\mathrm{.}341kg$

Length $L=0\mathrm{.}452m$

The ball reaches the vertically up position with zero speed.

What then is its speed at $($b$)$ the lowest point and $($c$)$ the point on the right at which the ball is level with the initial point?

$-($d$)$ If the ball's mass were doubled, would the answers to $($a$)$ through $($c$)$ increase, decrease, or remain the same?

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