velocity of a falling ball help

**Tweety** · February 25th 2013, 02:47 AM

In our simple model of the fight of a ball, the height
y above the foor at time t is

$y = V_{n}t-\frac{1}{2}gt^{2}$

where g is the acceleration due to gravity and vn is the velocity immediately after the nth bounce.

The maximum height of the ball is reached when dy/dt = 0
Find the time
tmax at which this maximum occurs and the maximum height
ymax that the ball reaches.

I am really not sure how to do this, since I do not know what vn is?

$\frac{dy}{dt} = V_{n} -gt = 0$

$V_{n} = gt$

dont know how to work ourt $y_{max}$

and $t_{max}$

**hollywood** · February 25th 2013, 07:11 AM

$t_{max}$ is the time when the derivative is zero, and you found the equation $V_n=gt$ for that. So you solve for t and get $t_{max}=\frac{V_n}{g}$ . Then you plug in to $y = V_{n}t-\frac{1}{2}gt^{2}$ to get the height at time $t_{max}$ , which is $y_{max}$ .

- Hollywood

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