You are firing a cannonball from the top of a cliff at a pir

You are firing a cannonball from the top of a cliff at a pirate ship which is behind a mountain. The height of the cannon is 100 m, the height of the mountain is 120 m, and the height of the pirate ship is 70 m. The mountain is horizontally 200 m away from cannon, while the pirate ship is horizontally 270 m away from the cannon. The speed of the cannonball after it is fired is 65 m s^-1. You could hit anywhere from the bottom of the pirate ship to the top in order to sink it. Over what angles could you fire the cannonball to sink the pirate ship?

Solution

Here ,

h1 = 100 m

h2 = 120 m

h3 = 70 m

x1 = 200 m

x2 = 270 m

u = 65 m/s

for the angle to cross the mountain

h2 - h1 = x2 * tan(theta) - g * x2^2/(2 * (v * cos(theta))^2)

-120 + 100 = 200 * tan(theta) - 9.8 * 200^2/(2 * (65 * cos(theta))^2

solving for theta

theta = 70.57 degree

the angle must be greater than 70.57 degree to hit the pirate ship