Question

a cannon is fired horizontally from the top of a castle and lands 250 meters down range. if the cannon ball leaves the cannon at 400 m/s how high is the castle?

Answer 1

Question#20775

a cannon is fired horizontally from the top of a castle and lands 250 meters down range. if the cannon ball leaves the cannon at 400 m/s how high is the castle?

Solution:

Let:

$$S = 250 \, \text{m}$$ $$v = 400 \, \text{m/s}$$

H-?

$$S = v t,$$

Were t is the time of free falling from height H

$$t = \frac{s}{v}$$

Such as:

$$H = \frac{1}{2} g t^2$$ $$=>$$ $$H = \frac{g s^2}{2 v^2}$$ $$H = \frac{9.8 \times 250^2}{2 \times 400^2} = 1.91 \, \text{m}$$

Answer: 1.91 m.