The radius of the wheel is 21 cm. When the wheel rotates once, the distance covered by the car is 2*pi*21.
As the wheel rotates at 800 RPM, it covers a distance equal to 2*pi*21*800 cm per minute.
The distance covered in one hour is 2*pi*21*800*60/100 m
=> 20160*pi m
=> 20.16*pi km
=> 63.33 km (approximately)
The required speed of the car is 20.16*pi or 63.33 km/hr.
The radius r of the wheel of the car = r = 21cm.
So in one rotation of the wheel, the distance the car moves = 2pi*r = 2pi*21/100 meter.
So the distance moved by the car in 800 RPM = 2pi*21*800/100 meter.
So the speed of the car per minute = 2pi*21*800/100 = 1055.575m.
So the speed of the car per hour = 1055.576*60/1000 km
= 63.33 kilo meter/ hour.
The formula of speed when knowing the number of rotations per minute is:
s = pi*D*n/1000
D = diameter of the wheel = 2*210 = 420 mm
pi = 3.14 approx
n = 800 rpm
Now, we'll introduce the data into the formula above:
s = 3.14*420*800/1000
We'll simplify and we'll get:
s = 3.14*42*8
s = 1055.04*60 minutes
s = 63302.4
s = 63.3 Km/hour