A 11 kg cannon ball is fired from a 630 kg brass cannon on a

A 11 kg cannon ball is fired from a 630 kg brass cannon on a frictionless, horizontal surface at an angle of 24º with respect to the horizontal. The cannon is constrained to move only in the horizontal direction. The initial velocity of the cannon ball is v_i = 37 m/s.

1) What is the x-component of the cannonball\'s momentum immediately after launch?

kg m/s

2) What is the y-component of the cannonball\'s momentum immediately after launch?

kg m/s

3) What is the recoil velocity of the cannon? Note this is a signed number, and positive indicates to the right.

m/s

Solution

1)

x component of cannon ball\'s momentum is

          p_x = m v_x

               = m v cos 24

               = (11 kg ) ( 37 m/s) cos 24

                = 371.82 kg.m/s

2)

y component of momentum

    p_y = m v_y

          = m v sin 24

          = ( 11 kg ) ( 37 m/s) sin24

          = 165.54 kg. m/s

3)

According to the conservation of momentum

         M V + p_x = 0

            V = - (371.82 kg.m/s ) / 630 kg

               =-0.59 m/s