The members of a high school basketball team are driving from calgary to vancouver,which is a distance of 675km.Each tire of their van has a radius of 32cm.If the team members drive at constant speed and cover the distance in 6h 45 min,what is the angular velocity,in radians/second,of each tire during the drive?

Well, if those basketball players want to know the angular velocity of their tires, they better get ready for a basketball-themed math joke!

Why did the basketball player bring a ladder to the game? Because he heard the game was going to be a "slam dunk"!

Now, let's get down to calculating that angular velocity!

First, we need to convert the distance from kilometers to centimeters, so 675 km = 675,000 cm.

Next, we'll need to convert the time from hours to seconds. Since there are 60 seconds in a minute and 60 minutes in an hour, we have:

6 hours = 6 * 60 * 60 = 21,600 seconds
45 minutes = 45 * 60 = 2,700 seconds

Adding those up, we get a total time of 24,300 seconds.

Now, we can calculate the total distance each tire travels by multiplying the circumference (2 * pi * radius) by the number of rotations made during the drive. The number of rotations can be calculated as the total distance divided by the circumference:

Distance = 675,000 cm
Circumference = 2 * pi * 32 cm

Number of rotations = Distance / Circumference

Finally, the angular velocity in radians/second can be calculated by dividing the total angle (2 * pi * Number of rotations) by the total time:

Angular velocity = (2 * pi * Number of rotations) / Total time

Now that we've made all these calculations, I hope those basketball players appreciate the "hoop"-la I've gone through to answer their question!

To find the angular velocity of each tire during the drive, we can use the formula:

Angular velocity (ω) = Distance / Time

First, let's convert the time to hours. 6 hours 45 minutes is equal to 6.75 hours.

Now, we need to find the distance covered by each tire. Since the van has four tires, the total distance covered by all four tires is 675 km. Therefore, the distance covered by each tire is:

Distance = Total Distance / Number of Tires = 675 km / 4 = 168.75 km

Since angular velocity is expressed in radians per second, we need to convert the distance from kilometers to meters:

Distance = 168.75 km * 1000 m/km = 168750 m

Next, we need to find the circumference of each tire using the formula:

Circumference = 2πr

where r is the radius of each tire.

Circumference = 2 * π * 0.32 m = 2.01 m (approx)

Finally, we can find the angular velocity of each tire by dividing the distance covered by the circumference of each tire:

Angular velocity = Distance / Circumference = 168750 m / 2.01 m ≈ 83831.34 rad

Therefore, the angular velocity of each tire during the drive is approximately 83831.34 radians/second.

To find the angular velocity of each tire during the drive, we need to consider the relationship between linear speed and angular speed.

The linear speed of an object moving along a circular path is given by the formula:

linear speed = angular speed * radius

In this case, the linear speed is the distance traveled divided by the time taken:

linear speed = distance traveled / time taken

Given that the distance traveled is 675 km and the time taken is 6 hours and 45 minutes, we need to convert the time into hours:

time taken = 6 hours + 45 minutes
= 6 + 45/60 hours
= 6.75 hours

Now, we can calculate the linear speed:

linear speed = 675 km / 6.75 hours
= 100 km/h

To calculate the angular velocity, we need to convert the linear speed from km/h to cm/s (since the radius is given in centimeters):

linear speed = 100 km/h * (100,000 cm/km) / (3600 s/h)
= 27.78 cm/s

Now, we can use the formula for linear speed to find the angular velocity:

angular speed = linear speed / radius

Given that the radius of each tire is 32 cm, we can calculate the angular velocity:

angular velocity = 27.78 cm/s / 32 cm
= 0.868 radians/second

Therefore, the angular velocity of each tire during the drive is approximately 0.868 radians/second.

675km/6.75hr = 100km/hr = 2778cm/s

tire circumference = 201cm
rotation speed is 2778/201 = 13.82 rev/s
12.82 * 2pi = 86.8 rad/s