A lighthouse is located on a cliff 150 meters above the sea level. The light from the lighthouse makes one full rotation every 30 seconds. How fast is the spot of light moving along the shoreline 1 minute after the light is turned on?
Guide On Rating System
Vote
To solve this problem, we need to find the speed at which the spot of light is moving along the shoreline.
One full rotation of the lighthouse light is completed in 30 seconds, which means the light travels a full circle in that time. Since we want to find the speed after 1 minute (60 seconds), we can determine how many full rotations the light makes in 60 seconds.
60 seconds / 30 seconds per rotation = 2 rotations
So, after 1 minute, the light makes 2 full rotations.
The distance traveled by the spot of light along the shoreline is equal to the circumference of each rotation, which can be calculated using the formula:
Circumference = 2πr
Where r is the radius of the full rotation. Since the lighthouse is located on a cliff 150 meters above sea level, the radius of the full rotation is equal to the distance from the cliff to the shoreline.
To find this distance, we can use the Pythagorean theorem:
r^2 = 150^2 + h^2
Where h is the horizontal distance from the cliff to the shoreline.
Since the lighthouse is located on the cliff, h is the same as the radius of the full rotation.
r^2 = 150^2 + r^2
Simplifying the equation:
2r^2 = 150^2
r^2 = (150^2) / 2
r^2 = 11250
r = √11250 ≈ 106.07 meters
Now that we have the radius of the rotation, we can calculate the circumference:
Circumference = 2πr
Circumference = 2π(106.07)
Circumference ≈ 2(3.14)(106.07)
Circumference ≈ 667.09 meters
Therefore, after 1 minute, the spot of light is moving along the shoreline at a speed of approximately 667.09 meters.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99