Question

You are a pirate working for Dread Pirate Roberts. You are in charge of a cannon that exerts a force 20,000 N on a cannon ball while the ball is in the barrel of the cannon. The length of the cannon barrel is 1.84 m, and the cannon is aimed at a 50-degree angle from the ground.(1) The acceleration of gravity is 9.8 m/s2. If Dread Pirate Roberts tells you he wants the ball to leave the cannon with speed v0= 76 m/s, what mass cannon ball must you use?(2) Assuming the Dread Pirate Roberts never misses, how far from the end of the cannon is the ship that you are trying to hit (neglect dimensions of the cannon)?

Answer 1

Answer:

Explanation:

Force $F=20,000 N$

Length of barrel $L=1.84 m$

launch angle $\theta =50$

velocity at the time of launch $v=76 m/s$

using $v^2-u^2=2 as$

$(76)^2=2\times a\times 1.84$

$a=1569.56 m/s^2$

mass $m=\frac{F}{a}=\frac{20,000}{1569.56}$

$m=12.74 kg$

(2)Range of ball

$R=\frac{u^2\sin 2\theta }{g}$

$R=\frac{(76)^2\sin 100}{9.8}$

$R=580.43 m$