# A cannon fires a cannonball horizontally with a speed of 488 m/s. A. How long will it take the cannonball to fall 40 ft? B. How far will the shot travel in this time?

Mar 7, 2014

A. 1.6 s; B. 770 m.

#### Explanation:

The range of the cannon is 770 m.

The shot is horizontal, so there is no initial vertical velocity.

A. How long will it take the cannonball to fall 40 ft?

40 ft × (0.305 m)/(1 ft) = 12 m

d = ½g t^2, where $d$ = distance, $g$ = acceleration due to gravity, and $t$ = time

$t = \sqrt{\frac{2 d}{g}} = \sqrt{\left(\text{2 × 12 m")/("9.81 m·s"^"-2}\right)} = 1.6 s$

B. How far will the shot travel in this time?

$d = v t$, where $v$ = velocity

 d = ("488 m")/("1 s") × 1.6 s ="770 m"

The range of the cannon is 770 m.