A passenger on a ride at the firemen's field days sits in a chair and is swung around at the end of a cable connected to a central tower. At full speed, the cable makes an angle of 56 degree with the vertical, and the chair is 46 m from the pole. What is the speed of the passenger?
To find the speed of the passenger, we need to use some trigonometry. Let's break down the information provided:
1. The cable connected to the central tower makes an angle of 56 degrees with the vertical.
2. The chair is located 46 meters from the pole.
We can use the fact that the vertical component of the speed at the end of the cable is zero. The horizontal component of the speed is equal to the speed of the passenger.
To solve the problem, we need to find the horizontal component of the total velocity at the end of the cable. We can use trigonometry to find the horizontal component.
Step 1: Draw a right-angled triangle with the angle of 56 degrees and the cable as the hypotenuse. Label the vertical side as the opposite side, the horizontal side as the adjacent side, and the cable as the hypotenuse.
Step 2: Use the trigonometric function cosine to relate the adjacent side and the hypotenuse:
cos(56 degrees) = adjacent side / hypotenuse
Step 3: Substituting the known values into the equation, we have:
cos(56 degrees) = adjacent side / 46 meters
Step 4: Solve for the adjacent side (which represents the horizontal component of the speed) by rearranging the equation:
adjacent side = cos(56 degrees) * 46 meters
Step 5: Calculate the horizontal component of the speed by multiplying the adjacent side by the speed (assuming the cable's length represents the speed of the passenger):
speed = cos(56 degrees) * 46 meters
By evaluating this expression, you can find the speed of the passenger.