# Linear velocity word problems?

Can anyone help me solve these word problems.

1. An automobile tire has a diameter of 30 inches how fast (r/m) does the wheel turn on the axle when the automobile maintains a speed of 45 mi/h?

2. If an automobile wheel 78 cm in diameter rotates 600 r/min what is the speed of the car in km/h?

• I know the radius for the second one is 39 so would I use the formula for v=r(omega)? – Chino Grande Jun 25 '12 at 20:08

## 1 Answer

The circumference of the wheel is $2.5\pi$ feet. At $45$ miles per hour, we are travelling at $\frac{(45)(5280)}{60}$ feet per minute.

So if $s$ is the number of revolutions per minute, we have $$(2.5\pi)s=\frac{(45)(5280)}{60},$$ and therefore $$s=\frac{(45)(5280)}{(60)(2.5\pi)}.$$ The rest can be done by calculator.

The other problem involves more or less the same ideas, but is a little easier. The circumference of the tire is $78\pi$ cm. At $600$ rpm, we travel $(78\pi)(600)$ cm per minute. This is $(78\pi)(600)(60)$ cm per hour. To convert to km per hour, divide by the number of cm in $1$ km, which is $100000$.

• I calculated, got $504.20286$. Maybe a glitch in handling the calculator? – André Nicolas Jun 25 '12 at 20:06
• how would I set up the second problem.I see I made a calc error with the first one. – Chino Grande Jun 25 '12 at 20:07
• I added to the answer. – André Nicolas Jun 25 '12 at 20:16
• The final answer in my book is 88.2 – Chino Grande Jun 25 '12 at 20:18
• I get $88.215922$. If you don't, you are not handling the calculator correctly. – André Nicolas Jun 25 '12 at 20:21