A shell is fired horizontally and takes .5 seconds to fall. If its initial speed were doubled, the time it would take to fall would be:

.25 seconds

I know the answer, but I need an explanation if possible.

Your answer is not correct.

Then what is the correct answer?

When the shell is fired horizontally, it has no vertical component. The vertical speed is 0. Gravity eventually pulls it to earth. If you double the horizontal speed, you still have no vertical component. Therefore, the time to fall is?

double?

If there is no vertical component, then the time to fall to earth is just a function of the height above ground. The shell always takes the same time to fall to the ground. If you double the initial speed of a horizontal shot, it still takes the same time before it strikes the ground. With the doubled speed the shell will travel farther, but the time to hit the ground is the same. If it was 0.5 seconds on the first shot, it will still be 0.5 seconds.

I understand now, thanks.

Sure! To understand why the time it takes for the shell to fall changes when its initial speed is doubled, let's break down the problem.

When the shell is fired horizontally, it has an initial horizontal velocity, which remains constant throughout its motion. Since the only force acting on the shell is gravity in the vertical direction, the shell will undergo vertical free fall.

In free fall, the time it takes for an object to fall depends solely on the vertical distance it travels and the acceleration due to gravity. On Earth, the acceleration due to gravity is approximately 9.8 meters per second squared (9.8 m/s^2).

In this case, when the initial speed of the shell is doubled, it means that its initial vertical velocity is also doubled. However, the acceleration due to gravity remains the same.

The time it takes for an object to fall vertically can be calculated using the formula:

t = sqrt(2h / g)

Where:
t = time taken to fall
h = vertical distance traveled
g = acceleration due to gravity

In this problem, since the shell is fired horizontally, we can assume that the vertical distance traveled is the same regardless of the initial velocity. Therefore, the only factor affecting the change in time is the acceleration due to gravity.

When the initial speed is doubled, the vertical velocity of the shell is doubled as well. However, the acceleration due to gravity remains the same. This means that the vertical distance traveled will also be doubled, resulting in a shorter time taken to fall.

Using the formula above, if the initial time taken to fall is 0.5 seconds, when the initial speed is doubled, the time taken to fall will be reduced to 0.25 seconds.

Therefore, when the initial speed of the shell is doubled, the time it takes to fall will be halved.