How Fast Must a Volleyball Be Hit to Clear the Net and Reach the Back Line?

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To determine the minimum velocity required for a volleyball to clear a 2.24m high net while being hit from a height of 3m and 8m away, calculations show an initial horizontal velocity of approximately 21.05 m/s. This velocity ensures the ball just clears the net at the peak of its trajectory. For the maximum velocity that allows the ball to strike the back line without going out of bounds, similar calculations must be conducted, adjusting for the distance to the back line. The approach involves analyzing the projectile motion equations and considering the time of flight. Accurate results depend on precise algebraic manipulation of the projectile motion formulas.
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Simple Projectile Question

there is a volleyball net 2.24m high (the court is 9m by 9m on both sides), and you hit the ball while being 3m in the air, you are 8m away from the net, if the initial velocity is horizontal find
A)what minimum velocity must the ball have to clear the top of the net
B)what maximum velocity can it have if the ball is to strike the the back line on the other side of the net?
Work...
V0 = ?
X-X0 = 8m
Y-Y0 = 0.76m
(theta) = 84.57
----------------------------------
Vy2 = -2g(y-y0)
Vy = 3.76m/s
Vy = V0sin(theta) - gt
Vy/-g = t
t = 0.38
X-X0 = V0x(t)
8m = V0x(0.38s)
V0x = 21.05 m/s?not likely
 
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I haven't run through the numbers, but your procedure looks good for part a.

You need to do something similar for part b. Just as in part a when you asked yourself what must V_{0x} be in order to clear the net, now you have to ask yourself what must V_{0x} be in order to not go past the edge of the court. The algebra is going to be the same, but with different numbers.
 
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