You are walking at 4.40 km per hour across a frozen lake in the snow. You do not realize that with each step you turn 0.40 degrees to your right. If your step length is 58.0 cm what is the diameter, in meters, of the circle that you are inadvertently tracing out?
After 360/0.40 = 900 steps, you will have completed a circle by varying your direction by 360 degrees.
The circumference that you will have walked will be 900*0.58 m = 522 meters
Divide by pi for the diameter.
The speed does not affect the answer.
To find the diameter of the circle that you are inadvertently tracing out, we can first calculate the radius of the circle using the information provided and then multiply it by 2 to get the diameter.
Let's break down the problem step by step:
Step 1: Calculate the number of degrees turned per step
We know that with each step, you turn 0.40 degrees to your right. Since you're walking at a constant speed, this degree of turning will occur with each step.
Step 2: Calculate the circumference of the circle
The circumference of a circle can be determined using the formula C = 2πr, where C is the circumference and r is the radius.
Since each step you take is equivalent to one round of the circle, the circumference of the circle will be the product of the step length and the number of steps it takes to complete one full round.
Step 3: Calculate the radius of the circle
Since the circumference of a circle is equal to 360 degrees, and each step corresponds to a turn of 0.40 degrees, we can find the number of steps required to complete a full rotation by dividing 360 degrees by 0.40 degrees.
The radius of the circle can be calculated by dividing the circumference of the circle by 2π.
Step 4: Calculate the diameter of the circle
The diameter of a circle is two times the radius. Multiply the radius by 2 to find the diameter.
Let's calculate the diameter of the circle:
Step 1: 0.40 degrees per step
Step 2: Circumference = Step length x Number of steps
Step 2: Circumference = 0.58 m x (360 degrees / 0.40 degrees)
Step 2: Circumference = 0.58 m x 900
Step 2: Circumference = 522 m
Step 3: Radius = Circumference / (2π)
Step 3: Radius = 522 m / (2 x 3.14)
Step 3: Radius ≈ 83.02 m
Step 4: Diameter = 2 x Radius
Step 4: Diameter = 2 x 83.02 m
Step 4: Diameter ≈ 166.04 m
Therefore, the diameter of the circle you are inadvertently tracing out is approximately 166.04 meters.