Projectile motion and pirate ship

[blimkie]

A pirate ship fires two shells at two identical enemy ships. Shell A hits ship A, which is close by, and shell B hits ship B, which is farther away. The shells are fired at the same speed; neglect air resistance. Select all the statements that are true; e.g., enter AB.


1. The shell fired at an angle closest to 45° always lands farther away.
2. The shell fired with an angle closer to the horizontal always has the longest range.
3. For two shells fired at the same angle, the heavier shell has less 'air time'.
4. The trajectory of the shells is a hyperbola.
5. The shell fired with an angle closer to the vertical has more `air time'.
6. Shells fired at angles θ and 90°−θ above the horizontal have the same range.

1. true
2. false
3. i initially thought this was true however my friend said this was false and his is correct
4. false...parabola
5. true i think but I am not sure
6. true

i verified 1 an 6 from diagrams in my book for projectiles of the same speed

 

[arildno]

To answer 5, you must find the time when the y-coordinate is zero again.
Write y as a function of time, set y=0, and solve the quadratic in time!

 

[kyle8921]

and angle, 4 is wrong because it is a parabola not a hyperbola, and 5 is true because the closer the angle is to the vertical, the longer the projectile will stay in the air before hitting the ground.