The Black Pearl has once again sailed into Port Royal and is firing its guns at the fort. The cannons atop the fort wall have been disabled, but there remains a single cannon at sea level which must defend the town. If the gunner estimates that the ship is 400 meters horizontally from the guns and he knows that the cannon has a muzzle velocity of 80 m/s, at what angle (or angles) should the cannon be aimed so as to hit the Black Pearl? Ignore air resistance, assume g = 9.8 m/s^2 and that the cannon and Black Pearl are at the same height above sea level.

Question

Note: Enter your answers as a single entry, a comma separated list or, if the cannonball cannot hit the ship, enter 'none'.

The cannon can be fired at
? degrees to hit the ship.

I've tried using 400 = 80 * t, solving for t to get 5, then going to the height formula and doing
0 * 5 - 9.81/2 * 5^2 = 122.625, then solving for the tangent. Doesn't work. The answer's either a single entry or comma separated list.

Answer 1

R = horizontal range (m)
v0 = initial velocity (m/s)
g = acceleration due to gravity (9.80 m/s2)
θ = angle of the initial velocity from the horizontal plane (radians or degrees)

R = v0 * sin(2θ) / g

Answer 2

forgot a small detail
... v0 is squared ... v0^2

Answer 3

Hey Scott,

Having a little trouble still.
80 = (400 * 9.8) / sin(2theta)
becomes sin2theta = 3920/6400, which is sin2theta = 0.6125
which is arcsin(0.6125 / 2)
which is 17.83, but my homework is still marking this as incorrect. Is there something additional I should be doing?

Thanks!