A group of soldiers hid at the bottom and against the wall of a 100 m. high cliff. Unknown to them, the Evil rebels have positioned a cannon on top of the cliff; 8,000 m. from the edge. If the cannon has a muzzle speed of 320 m/sec, how close to the bottom edge of the cliff can the shell reach ?
To determine how close to the bottom edge of the cliff the shell can reach, we need to calculate the horizontal distance traveled by the shell from the cannon's position to the bottom edge of the cliff.
We can use the horizontal motion equation:
Distance = Speed × Time
First, let's calculate the time it takes for the shell to reach the bottom edge of the cliff. Since the vertical distance is not provided and hasn't been specified as a factor affecting the shell's trajectory, we can assume the shell follows a parabolic path in the horizontal direction. Hence, the time taken for the shell to reach the bottom edge of the cliff will be the same as the time taken for it to reach the ground if it was fired horizontally.
The equation to calculate the time of flight for a projectile fired horizontally is:
Time = Distance / Speed
Given that the distance is 8,000 m and the speed is 320 m/sec, we can substitute these values into the equation:
Time = 8,000 m / 320 m/sec
Time = 25 seconds
So, we have determined that it takes 25 seconds for the shell to reach the bottom edge of the cliff.
Now, let's determine the horizontal distance traveled by the shell during this time. We can use the equation:
Distance = Speed × Time
Given that the speed of the shell is 320 m/sec and the time is 25 seconds, we can calculate:
Distance = 320 m/sec × 25 seconds
Distance = 8,000 meters
Therefore, the shell can reach a distance of 8,000 meters from the cannon's position, which means it can hit the bottom edge of the cliff.