As a horse archer in the armies of Genghis Khan, you are able to shoot enormous

Question

As a horse archer in the armies of Genghis Khan, you are able to shoot enormous distances by firing forward from the back of a galloping horse. Suppose that the speed of the arrow off the bowstring = is Vb=40.0m/s and the horizontal speed of the horse Vh=16.0 m/s. The range of your shot is measured on level ground from the point of the shot to the point where the arrow falls. Neglect all aerodynamic effects and the height of horse and rider. Do not worry about the effects of gravity while the bow is launching the arrow; the acceleration provided by the bowstring is much greater. Afterwards, use g=9.81 m/s^2 for the acceleration of gravity. Assume the arrow leaves the bow at the angle thetab at which it is pointed, in the reference frame of the archer.                                                          a.) Calculate the angle thetab at which you should aim for maximum range. HINT: Do not assume this will necessarily be thetab= 45 degrees , as it would for an archer on the ground.                         b.) Calculate the resulting maximum range Rgg of the shot.                                        c.) Calculate the maximum ground-to-ground range an archer standing on the ground, using the same bow, can obtain. Again, neglect the height of the archer. How much additional range does the mounted archer gain?

Explanation / Answer

a.)

Range (R) = v^2 sin(2theta)/g

at theta = 45 sin(2theta) would be maximum

so at theta = 45 the Range will be maximum

b.)Range (R) = v^2 sin(2theta)/g { V = 40 + 16 = 56 m/s Sin(2theta) = 1 }

Range = 56^2 /9.81 = 319.67 m

c.) Range (R) = v^2 sin(2theta)/g

R = 40^2 /9.81 = 163.09 m

additional range does the mounted archer gain? = 319.67 m - 163.09 m = 156.57 m

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