A projectile is fired horizontally from a launching device, exiting with a speed vx. While the projectile is in the launching device, the impulse imparted to it is Jp, and the average force on it is Favg. Assume the force becomes zero just as the projectile reaches the end of the launching device. Express your answers to parts (a) and (b) in terms of Ux, Tp, Favg, and fundamental constants, as appropriate. (a) Determine an expression for the time required for the projectile to travel the length of the launching device. (b) Determine an expression for the mass of the projectile. The projectile is fired horizontally into a block of wood that is clamped to a tabletop so that it cannot move. The projectile travels a distance d into the block before it stops. Express all algebraic answers to the following in terms of d and the given quantities previously indicated, as appropriate. (c) Derive an expression for the work done in stopping the projectile. (d) Derive an expression for the average force Fo exerted on the projectile as it comes to rest in the block. Now a new projectile and block are used, identical to the first ones, but the block is not clamped to the table. The projectile is again fired into the block of wood and travels a new distance d into the block while the block slides across the table a short distance D. Assume the following: the projectile enters the block with speed vx , the average force F, between the projectile and the block has the same value as determined in part (d), the average force of friction between the table and the block is fr, and the collision is instantaneous so the frictional force is negligible during the collision. (e) Derive an expression for d, in terms of d, D, f1, and Fo, as appropriate. (f) Derive an expression for d, in terms of d, the mass m of the projectile, and the mass M of the block.