A cannon ball (mass = ) is fired at a target of away. The cannon recoils by . Assuming the cannon ball moves with constant velocity, when will it hit the target? [Resistance offered by ground to cannon is ]
Step 1. Given data:
Mass of cannon ball =
Mass of cannon =
Distance of target =
Recoiling of cannon =
Resistance offered by ground to cannon =
Step 2. Formula used:
, where are velocities of cannon ball and cannon respectively.
2. Work done by the ground on the cannon is given by
Where is the distance of the recoil of the cannon and is the resistive force.
3. According to the law of conservation of kinetic energy between the ground and cannon, we get work done by the ground on the cannon is equal to the kinetic energy of the cannon immediately after firing.
Step 3. Calculations:
Putting the known values in the above formulas one by one, we get
All the K.E acquired by the cannon will be dissipated in overcoming the frictional force.
Hence
Putting the value of in , we get
Therefore time is taken by the cannonball to hit the target .