Question

Chris has a part time job as a cannon ball catcher for the circus. One day he was located an unknown distance away from the cannon. A cannonball was fired from the cannon at 425 m/s. The speed of sound was 345 m/s. Unfortunately the cannonball went past Chris 0.20 s before he heard the sound of the blast. How far away was the cannon from Chris?

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Answer 1

Answer: 366.56 meters.

Explanation:

Velocity of the cannon ball = 425m/s

Velocity of sound = 345 m/s

For the "position" of both, we have the equation:

Pc = 425m/s*t

Ps = 345m/s*t

Where t is time in seconds.

If the position of Chris is X, we have that if the ball reaches the position of Chris in T seconds, then the soundwave reaches the position of Chris in T + 0.20 seconds, we can write this as:

425m/s*T = X

345m/s*(T + 0.20s) = X

Now we can solve this system of equations. First we can replace the first equation in the second equation and get

345m/s*(T - 0.20s) = 425m/s*T

Now we solve this for T.

345*T + 69 = 425*T

69 = (425 - 345)*T = 80*T

T = 69/80 = 0.8625 seconds.

Now we replace this in the first equation and get:

X = 425m/s*T = 425m/s*0.8625s =  366.56 meters.