A submersible traveling at a depth of 250 feet dives at an angle of 15 degrees with respect to a line parallel to the water's surface. It travels a horizontal distance of 1500 feet during the dive. What is the depth of the submersile after the dive?Explain how the angle of the dive affects the final depth.

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To find the depth of the submersible after the dive, we can break down the distance traveled into its horizontal and vertical components.

First, let's find the horizontal distance traveled. The submersible travels a horizontal distance of 1500 feet during the dive.

Next, let's find the vertical distance, which is the depth of the submersible after the dive. The angle of the dive is given as 15 degrees with respect to a line parallel to the water's surface.

We can use trigonometry to find the vertical distance. The trigonometric function we will use is the sine function, which relates the lengths of the sides of a right triangle.

The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the opposite side is the vertical distance (depth), and the hypotenuse is the distance traveled.

The formula to find the vertical distance is: vertical distance = distance traveled * sin(angle)

Plugging in the given values, we have:
vertical distance = 1500 feet * sin(15 degrees)

Now, we can calculate the vertical distance, which represents the depth of the submersible after the dive.

However, it's important to note that the angle of the dive affects the final depth. If the submersible dives straight down (angle of 0 degrees), the vertical distance (depth) will be equal to the distance traveled. But as the angle increases, the vertical distance decreases, meaning the submersible will be shallower.

In this particular case, if the submersible dives at an angle of 15 degrees, the depth will be less than the distance traveled. This is because part of the distance traveled is used to create the horizontal component of motion, resulting in a shallower depth.