A muzzleloading cannon has a maximum projectile velocity of 300. m/s. If the speed of
sound in air is 340. m/s and the target is 1200. m away from the cannon, how much warning will
the target have, assuming that it can't see the cannon?
t sound = x/vs
t cannonball = x/vc
difference is warning time
To determine the amount of warning the target will have, we need to calculate the time it takes for the projectile to travel the distance of 1200 m. We can do this by dividing the distance by the speed of the projectile.
First, let's calculate the time it takes for the projectile to reach the target:
Time = Distance / Speed
Time = 1200 m / 300 m/s
Time = 4 seconds
So, the projectile will take 4 seconds to reach the target.
Now, let's calculate the time it takes for the sound of the cannon firing to reach the target:
Time = Distance / Speed
Time = 1200 m / 340 m/s
Time = 3.53 seconds (rounded to two decimal places)
Therefore, the target will have approximately 3.53 seconds of warning before the projectile hits it.