Help on a trigonometry question

Question

a trucks 34-in diameter wheels are turning at 450 rpm find the linear speed of the truck in mph,

Answer 1

about 45.51739356 mph for a truck wheel diameter 34 inches turning 450 rpm

it goes 34pix450 inches per minute

= 34pix450/12 feet per minute

= 34pix450/12x5280 miles per minute

= 34pix450x60/12x5280 mph

= about 46 mph rounded to nearest integer

= exactly 14.488636363...pi miles per hour= 1275pi/88 mph

Answer 2

To find the linear speed of the truck in mph, we can use the relationship between the rotational speed of the wheels and their linear speed.

Determine the circumference of the wheel: The circumference C of the wheel is given by: C = π × d,

where d is the diameter of the wheel.

Given d = 34 inches, we have:

C = π×34 ≈ 106.81 inches.

Find the linear speed in inches per minute: The linear speed v of the truck is the distance the truck travels in one minute. It is given by:

v=circumference × revolutions per minute

So, v=106.81 × 450 ≈ 48064.5 inches per minute.

Convert inches per minute to miles per hour: To convert the speed to mph, we need to convert inches per minute to miles per hour.

1. There are 12 inches in a foot, and 5280 feet in a mile, so there are 12 × 5280 = 63360 inches in a mile.
2. There are 60 minutes in an hour.

Therefore,

Speed in mph = (48064.5 inches per minute​ / 63360 inches per mile) × 60 minutes per hour

Speed in mph ≈ (48064.5 / 63360) × 60 ≈ 45.51 mph

So, the linear speed of the truck is approximately 45.51 mph.