Part 2
You are a pirate working for Dread Pirate
Roberts. You are in charge of a cannon that
exerts a force 20000 N on a cannon ball while
the ball is in the barrel of the cannon. The
length of the cannon barrel is 2.19 m and
the cannon is aimed at a 32◦
angle from the
ground.
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 =86 m/s, what mass cannon ball must you use?
Answer in units of kg.
Part 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 cannon)?
Answer in units of m.
To find the mass of the cannon ball, we can use the equation:
Force = mass * acceleration
In this case, the force exerted on the cannon ball is 20000 N. The acceleration of gravity is 9.8 m/s^2. Let's plug in these values:
20000 N = mass * 9.8 m/s^2
To solve for mass, we divide both sides of the equation by 9.8 m/s^2:
mass = 20000 N / 9.8 m/s^2
mass = 2040.82 kg
Therefore, the mass of the cannon ball must be approximately 2040.82 kg.
-------------------
To determine how far from the end of the cannon the ship is, we can use the range formula for projectile motion:
Range = (v0^2 * sin(2θ)) / g
In this case, the initial velocity (v0) is 86 m/s and the angle (θ) is 32 degrees. The acceleration due to gravity (g) is 9.8 m/s^2. Let's plug in these values:
Range = (86^2 * sin(2 * 32)) / 9.8
Using a calculator, we find:
Range ≈ 924.72 m
Therefore, the ship is approximately 924.72 meters away from the end of the cannon.