I need help with solving these word problems.

Marion rides her racing bicycle @ speed of 8 m/s. Bicycle wheels have a radius of 34 cm. What is the angular speed of wheels? How many times does each wheel go around during a 10-min race?

A car tire has radius of 33cm. Tire turns a total of 10,250 radians during trip to store. How many meters did car travel?

To solve these word problems, we need to understand some basic concepts and formulas related to angular speed and distance.

1. Angular speed:
Angular speed is the rate at which an object rotates or moves along a circular path. It is usually measured in radians per second (rad/s). The formula to calculate angular speed is:
Angular speed (ω) = linear speed (v) / radius (r)

2. Distance covered:
The distance covered by a rotating object can be calculated using the formula:
Distance = angular displacement × radius

Now, let's solve the word problems one by one:

Word problem 1: Marion's racing bicycle
Marion rides her racing bicycle at a speed of 8 m/s. The bicycle wheels have a radius of 34 cm. We need to find the angular speed of the wheels and the number of times each wheel goes around during a 10-minute race.

Step 1: Calculate the angular speed:
Angular speed (ω) = linear speed (v) / radius (r)
= 8 m/s / 0.34 m (34 cm = 0.34 m)
= 23.53 rad/s (rounded to two decimal places)

So, the angular speed of the wheels is 23.53 rad/s.

Step 2: Calculate the number of times each wheel goes around in a 10-minute race:
We know that time = 10 minutes = 600 seconds.
The total number of revolutions per wheel can be calculated using the formula:
Number of revolutions = angular speed × time / (2π)

Number of revolutions = 23.53 rad/s × 600 s / (2π)
= 590.27 revolutions (rounded to two decimal places)

So, each wheel goes around approximately 590.27 times during a 10-minute race.

Word problem 2: Car tire's distance traveled
A car tire has a radius of 33 cm and it turns a total of 10,250 radians during the trip. We need to find the distance traveled by the car.

Step 1: Calculate the distance covered:
Distance = angular displacement × radius
= 10,250 rad × 0.33 m (33 cm = 0.33 m)
= 3,382.5 m (rounded to one decimal place)

So, the car traveled approximately 3,382.5 meters during the trip.

These are the solutions to the word problems. If you encounter any difficulties, please let me know.

To find the angular speed of the bicycle wheels, we can use the formula:

Angular speed (ω) = linear speed (v) / radius (r)

Given that the linear speed (v) of Marion's bicycle is 8 m/s and the radius (r) of the wheels is 34 cm, we first convert the radius to meters:

Radius (r) = 0.34 m

Now we can calculate the angular speed:

Angular speed (ω) = 8 m/s / 0.34 m
≈ 23.53 rad/s (rounded to two decimal places)

So, the angular speed of the bicycle wheels is approximately 23.53 rad/s.

To find the number of times each wheel goes around during a 10-minute race, we can use the formula:

Number of revolutions = (linear distance traveled) / (circumference of the wheel)

We know that the linear speed is 8 m/s and the time is 10 minutes. To find the linear distance traveled, we multiply the linear speed by the time:

Linear distance traveled = 8 m/s × (10 minutes × 60 seconds/minute)
= 8 m/s × 600 seconds
= 4800 meters

The circumference of the wheel can be calculated using the formula:

Circumference = 2π × radius

Given that the radius is 34 cm, we convert it to meters first:

Radius (r) = 0.34 m

Circumference = 2π × 0.34 m
≈ 2.13 m (rounded to two decimal places)

Now we can calculate the number of revolutions:

Number of revolutions = 4800 meters / 2.13 meters
≈ 2254.98 (rounded to two decimal places)

Therefore, each wheel goes around approximately 2254.98 times during a 10-minute race.

Next, let's solve the second word problem:

To find the distance traveled by the car, we can use the formula:

Distance (d) = angular displacement (θ) × radius (r)

Given that the angular displacement (θ) of the tire is 10,250 radians and the radius (r) is 33 cm, we convert the radius to meters:

Radius (r) = 0.33 m

Now we can calculate the distance traveled:

Distance (d) = 10,250 radians × 0.33 m
≈ 3,382.5 meters (rounded to one decimal place)

Therefore, the car traveled approximately 3,382.5 meters during the trip to the store.