Posted by Isis on Thursday, November 29, 2012 at 6:22pm.
y = y0 + v0*t - 1/2*g*t^2
where y0 is the initial height = 0, v0 is the initial speed, and g is the acceleration due to gravity, t is time, and y is the vertical position.
The ball reaches it's maximum height when dy/dt = 0 = v0 - g*t
and y = 5, so
5 = v0*t - 1/2*g*t^2
Use algebra to find the initial velocity and time.
The final velocity of the ball is given by
1. v = v0 - g*t, occurs when y = 0, or when
2. 0 = v0*t - 1/2*g*t^2
solve 2nd equation for t, and plug into 1st equation to solve for the final speed v at this time.
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