A cannon is placed on level ground, shooting cannonballs that land on the ground. We will...

  

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A cannon is placed on level ground, shooting cannonballs that land on the ground. We will show here that the largest range R is obtained when the angle is 45 degrees. (a) Using the equations for projectile motion, determine the range R(0) as a function of the angle 0. To make things simpler, let x = 0 here. Your answer should only contain the symbols Vox, Voy, and/or g. (b) Instead of using Vox and voy, write the expression you found in part (a) in terms of initial speed vo and launch angle 0. Simplify your answer using the trig identity sin cos 0=sin(20). Your answer should not contain any other symbols than vo, 6, and/or g. (c) Take the derivative of R(6). In other words, find dR/de. (d) Use dR/de to find the angle that gives the maximum range. Hint: remember that a function f(x) has a maximum (or minimum) at xm when the derivative f'(xm) is equal to zero. A cannon is placed on level ground, shooting cannonballs that land on the ground. We will show here that the largest range R is obtained when the angle is 45 degrees. (a) Using the equations for projectile motion, determine the range R(0) as a function of the angle 0. To make things simpler, let x = 0 here. Your answer should only contain the symbols Vox, Voy, and/or g. (b) Instead of using Vox and voy, write the expression you found in part (a) in terms of initial speed vo and launch angle 0. Simplify your answer using the trig identity sin cos 0=sin(20). Your answer should not contain any other symbols than vo, 6, and/or g. (c) Take the derivative of R(6). In other words, find dR/de. (d) Use dR/de to find the angle that gives the maximum range. Hint: remember that a function f(x) has a maximum (or minimum) at xm when the derivative f'(xm) is equal to zero.