I know a professor from Alfred State College that gives problems like this. I just don't see the point in hitting students over the head with problems that, yes they ought to be able to do but that, have such a large number of steps before they can check to see if they have a reasonable answer.

And yes, I know the Europeans do it constantly, but I questionanyinstructor who teaches the SI system of units and gives aweightin kg.

To the problem.

I'll give you the overview and you can fill in the missing steps. As with many problems where you know the final information, you need to work backward.

1) We need to know how fast the tank is initially moving so that it has a speed of 0 m/s at the very edge of the cliff. This is a simple 1 - D motion problem where the tank has a constant deceleration of 3 m/s^2.

2) We know how fast the tank needs to be moving after the collision with the projectile. The collision is perfectly inelastic (the two objects move as one at the end of the collision), and the tank is initially not moving. So find the speed of the projectile just before it hits the tank. Use Conservation of Momentum here (and at all other times) not Conservation of Energy. Energy isnotconserved in this kind of collision, I don't care what your homework problem says about it.

3) We aren't really given enough information for the flight of the projectile to be 2 - D motion. (We'd need to know the angle the gun was firing at, for instance.) This is why I called what you were looking for in 2) as "the speed" rather than "the horizontal component of the velocity." So assume 1 - D motion. You know the constant (average, really) deceleration of the projectile over the 100 m range, and you know from 2) what the speed of the projectile must be at the end of this run. We want the initial speed of the projectile.

This answers the first question.

4) We know the speed of the bullet just after it leaves the barrel from 3). Assume the total mass of the gun is in the barrel. (We are given no information about the gun itself so this is necessary.) The total momentum of the system (gun and projectile) is 0 kgm/s before the gun was fired and we know the momentum of the projectile after it was fired. So this is the momentum (in the opposite direction) the gun has after it was fired. So you can find the speed of the recoil of the gun.

5) You know the speed of recoil from 4) and you know that the gun will experience a constant deceleration in 1 - D of 20 m/s^2. So you can find how far it travels.

Good luck!

-Dan