If a tire rotates at 150 revs/min when the truck is travelling 40km/h, what is the circumference of the tire?
4.44 meters
To solve this question, you need to know the relationship between the tire's rotational speed (revolutions per minute) and the truck's linear speed (kilometers per hour). The circumference of the tire can be calculated using this relationship.
Step 1: Convert the truck's speed from kilometers per hour to meters per minute:
To convert from kilometers per hour to meters per minute, you need to multiply the speed by a conversion factor. There are 60 minutes in an hour, and 1000 meters in a kilometer. So, the conversion factor is (1000 meters/1 kilometer) / (60 minutes/1 hour), which simplifies to 1000/60 = 16.67.
Therefore, 40 km/h * 16.67 = 666.8 meters/minute.
Step 2: Determine the distance travelled by the tire in one revolution:
Since the tire rotates a certain number of revolutions per minute, we need to find out how much distance the tire covers in one revolution. This distance is equal to the circumference of the tire.
Let's denote the circumference of the tire as C.
Step 3: Calculate the tire's rotational speed:
The rotational speed of the tire is given as 150 revs/min.
Step 4: Relate the tire's linear speed and rotational speed:
The linear speed of the truck can be related to the rotational speed of the tire using the formula:
Linear speed = rotational speed * circumference of the tire
In this case, the tire rotates at 150 revs/min, and the truck's speed is 666.8 meters/minute.
So, we can write the equation as: 666.8 m/min = 150 revs/min * C.
Step 5: Solve for C:
To find the circumference of the tire (C), divide both sides of the equation by 150 revs/min:
C = 666.8 m/min / 150 revs/min.
Calculating the right side of the equation gives us: C ≈ 4.45 meters (rounded to two decimal places).
Therefore, the circumference of the tire is approximately 4.45 meters.
40km/hr = 40/60 km/min = 40000/60 m/min
40000/60m/min / 150rev/min = 40000/9000 m/rev = 40/9 m/rev = 4.44 m/rev