Question

a small trading coaster is trying to break from port that is gaurded by cannon mounted 500m above sea level on a cliff overlooking the prot. the coaster's mass is 2000kg and has a sail area that allows a force of 65N to effect the coaster. the max velocity of the coaster is 5m/s . the coaster starts at 50 m from the base of the cliff. the cannon has two charges .one that fires a cannon ball at 15m/s and a second one at 75m/s the cannon cannot be elevated. find:

1-cannon's effective min and max rane

2-the cannons balls time of flight

3-the time it takes the coaster to escape

4-the time that the cannon could fire and hit the coaster (two possible answers)

Answer 1

1. time of flight will be: (2*500/10)^0.5 = 10 s

So, Max range : 750m and min range = 150m

2. 10s

3. v=5 m/s will be acheived at t= 153.846 s

distance covered during this time = 50 + (0.5*0.0325*153.846*153.846) = 434.614 m

remaining distance will be covered in 63.07 s

So, total time = 216.92 s

4. First case, min range case: 150 =50 + (0.5*0.0325*t*t)

=> t= 78.446 . So, fire cannon at t= 68.446 s

Second case, MAx range case: fire at t=216.92-10= 206.92 s