1.) Pirates fire a projectile from a cannon at an initial velocity of 55.0 m/s a

Question

1.) Pirates fire a projectile from a cannon at an initial velocity of 55.0 m/s and an initial angle 30.0 degrees above the horizontal. Assuming air resistance is negligible and the cannon is located at x=0, y=0:

a.) What is the maximum height of the cannonball? (7 pts)

b.) How far does the projectile travel in the x-direction before landing (returning to y=0)? (7 pts)

c.) Suppose the projectile is actually composed of 2 balls linked by a chain that breaks into 2 parts mid-flight. If one part contains 40% of the total mass and lands at a position x=410 m, where does the other part containing 60% of the total mass land according to the principle of center of mass? (6 pts)

Explanation / Answer

a) max hieght = v^2sin^2(theta)/2g = 55^2*sin^2(30)/2*g = 38.584 m
b) range = v^2sin(2*theta)/g = 267.319 m
c) The com lands at the above range
   0.4*(410 - 267.319) = 0.6(267.319 - x)
   x = 172.198 m

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