You are a contestant on a TV reality game show where you and yourteam are given

Question

You are a contestant on a TV reality game show where you and yourteam are given a
challenge to use an air-gun to shoot a ball and hit a target 30.0meters away on flat
horizontal ground in two shots. The air gun fires the ball at thesame velocity every
time but you can adjust the angle that it shoots at. You remembersomething from
physics class bout 45 degrees being the “optimal” angleso you take your first shot with the
gun set at an angle of 45 degrees above the horizontal. That shotsails 5.5 meters beyond the
target. You’ve got one more shot to win and big money is onthe line. What do you
do?

Explain why there is more than one correct answer between 0 degreesand 90 degrees
with respect to the horizontal for the angle of the air gun.

Explanation / Answer

You are a contestant on a TV reality game show where you and yourteam are given a challenge to use an air-gun to shoot a ball and hit a target 30.0meters away on flat horizontal ground in two shots. The air gun fires the ball at thesame velocity every time but you can adjust the angle that it shoots at. You remembersomething from physics class bout 45 degrees being the “optimal” angleso you take your first shot with the gun set at an angle of 45 degrees above the horizontal. That shotsails 5.5 meters beyond the target. You’ve got one more shot to win and big money is onthe line. What do you do? target range=30m when shot at 45 degree which has the probability of maximum rangeit reaches 35.5m hence u*u/g=35.5m now u=initial velocity=18.65m/sec now he has to aim for range=30m u=18.65m/sec range=18.65*18.65*sin2/g=30 calculating sin2=30*9.8/18.65*18.65=0.8452 so angle of projection should be 28.84degree. Explain why there is more than one correct answer between 0 degreesand 90 degrees with respect to the horizontal for the angle of the air gun. range=u*usin2/g sin2=sin(180-2) hence range=u*usin2/g range=u*usin(180-2)/g=u*usin2(90-)/g so we are getting the same value for range for two angles ofprojection 1) 2)90- that is why we are getting two values of projection between 0 and90 degree. in the above case he can project at an angle of 28.84 or(90-28.84)=61.16degrees.

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