Two boats leave at an angle of 25 pie/36 radians, one has a speed of 100km/hr and the second has a speed of 65 km/hr. How far apart are they after two hours?
To find out how far apart the boats are after two hours, we can use the concept of relative velocity.
First, let's convert the angle from radians to degrees. We know that π radians is equal to 180 degrees, so 25π/36 radians will be approximately equal to (25 * 180) / 36 degrees, which simplifies to 125 degrees.
We can now break down the velocities of the two boats into their horizontal and vertical components using trigonometry.
For the boat with a speed of 100 km/hr:
- The horizontal component of its velocity is 100 * cos(125°).
- The vertical component of its velocity is 100 * sin(125°).
For the boat with a speed of 65 km/hr:
- The horizontal component of its velocity is 65 * cos(0°).
- The vertical component of its velocity is 65 * sin(0°).
Since the horizontal component of the second boat is 65 * cos(0°) and the horizontal component of the first boat is 100 * cos(125°), we subtract the two to get the total horizontal separation after two hours.
Similarly, since the vertical component of the second boat is 65 * sin(0°) and the vertical component of the first boat is 100 * sin(125°), we subtract the two to get the total vertical separation after two hours.
Finally, we can calculate the distance between the two boats using the Pythagorean theorem, which states that the square of the hypotenuse (distance) of a right triangle is equal to the sum of the squares of the other two sides (horizontal and vertical separation).
Let's plug in the values and calculate step by step.
Horizontal separation of the two boats after two hours:
100 * cos(125°) - 65 * cos(0°)
Vertical separation of the two boats after two hours:
100 * sin(125°) - 65 * sin(0°)
Distance between the two boats after two hours:
√[(Horizontal separation)^2 + (Vertical separation)^2]
Please note that the trigonometric functions (cos and sin) take arguments in radians. Make sure to use the appropriate conversion if you're working with degrees.