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Solved: A 3000-kg cannon is mounted so that it can recoil

Chapter 8, Problem 47

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QUESTION:

 Problem 47PE

A 3000-kg cannon is mounted so that it can recoil only in the horizontal direction. (a) Calculate its recoil velocity when it fires a 15.0-kg shell at 480 m/s at an angle of 20.0º above the horizontal. (b) What is the kinetic energy of the cannon? This energy is dissipated as heat transfer in shock absorbers that stop its recoil. (c) What happens to the vertical component of momentum that is imparted to the cannon when it is fired?

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QUESTION:

 Problem 47PE

A 3000-kg cannon is mounted so that it can recoil only in the horizontal direction. (a) Calculate its recoil velocity when it fires a 15.0-kg shell at 480 m/s at an angle of 20.0º above the horizontal. (b) What is the kinetic energy of the cannon? This energy is dissipated as heat transfer in shock absorbers that stop its recoil. (c) What happens to the vertical component of momentum that is imparted to the cannon when it is fired?

ANSWER:

Solution to  47PE

Step 1 of 5

We need to calculate the recoil velocity of a 3000kg canon which can recoil only on horizontal direction. We have to find the kinetic energy of the canon and we have to comment on the vertical component of momentum when the shell is fired.

According to the conservation of momentum, the net change in momentum is zero,

 is the initial momentum of canon

 is the initial momentum of shell

 final momentum of canon

 final momentum of shell.

Free body diagram:

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