Problem: The Long Range Volleyball You climb to the top of a huge antenna tower,

Question

Problem: The Long Range Volleyball

You climb to the top of a huge antenna tower, of height 490 m above level ground. You serve a volleyball horizontally outwards from the tower. How fast must the speed of your serve be, in order for the volleyball to hit the ground 400 m away from the base of the tower? Neglect air resistance.

And then your friend stands on the ground at the spot where the volleyball hits, and tries to serve the ball back to you at the top of the tower, hitting the ball at the same angle to the ground as it arrived at. How fast must that serve be? Again, neglect air resistance.

Is it humanly possible to serve a volleyball that fast, either from the top, or from the ground? Possibly useful numbers:

g = 9.8 m/s2
1 mph = 0.447 m/s

Explanation / Answer

y = ut+ 0.5 gt^2 =>490 =0+ 0.5 *9.8 t^2 => t =10s velocity given to ball at top = 400/10 = 40m/s tan(theta) =490/400 => theta= 50.77 degrees let velocity given to ball at the bottom is v' so, v' cos (theta) = 400/t' and v =u+ at => 0= v' sin(theta) -9.8 t => v' sin(theta) = 9.8 (400/v*cos(theta)) => v' = 89.44 m/s No, it is not humanly possible to give the ball such a high speed.

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