The wheels of a car have radius 11 in. and are rotating at 800 rpm. Find the speed of the car in mi/h.
mi/h
To find the speed of the car in miles per hour, we can use the formula:
Speed (in mi/h) = 2πr × rpm × 60 ÷ 5280,
where r is the radius of the wheel in feet and rpm is the rotations per minute.
Given that the radius of the wheel is 11 inches, we convert it to feet by dividing by 12:
r = 11 ÷ 12 = 0.91667 ft.
Substituting r = 0.91667 ft and rpm = 800 into the formula:
Speed (in mi/h) = 2π(0.91667) × 800 × 60 ÷ 5280.
Calculating this expression will give us the speed of the car in miles per hour:
Speed (in mi/h) = 2π(0.91667) × 800 × 60 ÷ 5280 = 2π(0.91667) × 800 ÷ 88 = 440 π ≈ 1382.4 mi/h.
Therefore, the approximate speed of the car is 1382.4 miles per hour.
To find the speed of the car in mi/h, we first need to find the linear speed of the wheels. The linear speed is the distance traveled along the circumference of the wheel per unit of time.
The formula for linear speed is:
Linear Speed = Circumference of the wheel × Number of rotations per unit of time
To find the circumference of the wheel, we can use the formula:
Circumference = 2π × Radius
Given that the radius of the wheels is 11 in., we can find the circumference using the formula:
Circumference = 2π × 11 in.
Next, we are given that the wheels are rotating at 800 rpm (rotations per minute). To convert rpm to rotations per hour, we can multiply by 60 (since there are 60 minutes in an hour):
Rotations per hour = 800 rpm × 60 min/hour
Now that we have the values for circumference and rotations per hour, we can calculate the linear speed:
Linear Speed = Circumference × Rotations per hour
Substituting the values, we get:
Linear Speed = (2π × 11 in.) × (800 rpm × 60 min/hour)
Simplifying the units, we have:
Linear Speed = (2π × 11 in.) × (800/1) × (60/1) in/hour
Simplifying the expression further, we get:
Linear Speed ≈ (2π × 11 × 800 × 60) in/hour
Finally, to convert the linear speed from inches per hour to miles per hour, we need to divide by the number of inches in one mile. There are 12 inches in a foot and 5280 feet in a mile, so:
Linear Speed (mi/h) ≈ (2π × 11 × 800 × 60) in/hour ÷ (12 × 5280)
Evaluating this expression will give us the answer in miles per hour.
circumference of wheel
= distance covered in 1 rotation
= 2π(11) = 22π inches
distance covered in 800 rotations
= 800(22π) = 17600π inches
= 17600π/12 ft
= 17600π/(12(5280)) miles
= .87266.. miles per minute
= 52.36 miles/hr