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Chapter 4: Problem 17

In the film "The World's Fastest Indian" Anthony Hopkins plays Burt Munro who reaches a velocity of 201 mph in his 1920 Indian motorcycle. (a) At this velocity, how far does the Indian travel in 10 s? (b) How long time does the Indian need to travel \(1 \mathrm{~km}\) ?

Short Answer

Expert verified
(a) 2944 feet. (b) 11.14 seconds.

Step by step solution

01

Convert Velocity from mph to fps

First, convert the velocity from miles per hour (mph) to feet per second (fps) using the conversion factors:1 mile = 5280 feet1 hour = 3600 seconds.Thus, velocity in fps is calculated as follows: \[201 \text{ mph} = 201 \times \frac{5280 \text{ feet}}{3600 \text{ seconds}} = 294.4 \text{ fps}\]
02

Calculate Distance in 10 Seconds

Use the formula for distance traveled: \[\text{Distance} = \text{Velocity} \times \text{Time}\]Substitute the values from Step 1 and the given time (10 seconds):\[\text{Distance} = 294.4 \text{ fps} \times 10 \text{ s} = 2944 \text{ feet}\]
03

Convert 1 km to feet

To find out how long it takes to travel 1 kilometer, first convert kilometers to feet. 1 kilometer is equal to 3280.84 feet.\[1 \text{ km} = 3280.84 \text{ feet}\]
04

Calculate Time to Travel 1 km

Using the formula for time taken:\[\text{Time} = \frac{\text{Distance}}{\text{Velocity}}\]Substitute the distance (3280.84 feet) and the velocity (294.4 fps): \[\text{Time} = \frac{3280.84 \text{ feet}}{294.4 \text{ fps}} \text{Time} ≈ 11.14 \text{ seconds}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Conversion of Units
When solving physics problems, especially in elementary mechanics, it's crucial to use consistent units. This means converting values from one unit system to another when necessary. For example, if distance is given in miles and time in seconds, you need to convert miles to feet or meters to match the time unit. In our exercise, we converted the speed from miles per hour (mph) to feet per second (fps). Knowing conversion factors is essential: 1 mile is 5280 feet, and 1 hour is 3600 seconds. This allows us to compute velocity in a more manageable unit for the calculations.
Distance Calculation
To find out how far an object travels over time, use the formula:

Distance = Velocity x Time

In our example, after converting Burt Munro's speed to fps (294.4 fps), we needed to determine the distance traveled in 10 seconds. By multiplying the velocity by the time, we get the distance:

294.4 fps x 10 seconds = 2944 feet.

So, the Indian motorcycle travels 2944 feet in 10 seconds at a velocity of 201 mph.
Velocity Conversion
Velocity conversion is a common step in mechanics problems. It involves transforming speed into different units to match the other values in a problem. In our example, Burt Munro's motorcycle speed was initially given in mph. To facilitate calculations, we converted it to fps. Here is how you can do it:

Multiply the speed by the conversion factor:
201 mph x (5280 feet / 1 mile) x (1 hour / 3600 seconds)

This simplifies to:

201 x 5280 / 3600 = 294.4 fps

This conversion is essential because using consistent units makes the math straightforward and less prone to error.
Time Calculation
Another vital aspect of elementary mechanics problems is calculating the time required for an event. This can often be derived using the basic kinematic equation:

Time = Distance / Velocity

For instance, to find out how long it takes the motorcycle to travel 1 kilometer, we first converted 1 km to feet (3280.84 feet). Then, we use the velocity we already converted to fps:

Time = 3280.84 feet / 294.4 fps ≈ 11.14 seconds

Thus, it takes approximately 11.14 seconds for the motorcycle to travel 1 kilometer. Understanding how to manipulate and use these basic equations is key to solving many elementary mechanics problems.

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Most popular questions from this chapter

A freight train travels from Oslo to Drammen at a velocity of \(50 \mathrm{~km} / \mathrm{h}\). An express train travels from Drammen to Oslo at \(200 \mathrm{~km} / \mathrm{h}\). Assume that the trains leave at the same time. The distance from Oslo to Drammen along the railway track is \(50 \mathrm{~km}\). You can assume the motion to a long a line. (a) When do the trains meet? (b) How far from Oslo do the trains meet?

An object starts at \(x=x_{0}\) with a velocity \(v=v_{0}\) at the time \(t=t_{0}\) and moves with a constant acceleration \(a_{0}\). Show that the velocity \(v\) when the object has moved to a position \(x\) is \(v^{2}-v_{0}^{2}=2 a_{0}\left(x-x_{0}\right)\).

When the heliobacter bacteria swims, it is driven by the rotational motion of its tiny tail. It swims almost at a constant velocity, with small fluctuations due to variations in the rotational motion. As a simple model for the motion, we assume that the bacteria starts with the velocity \(v=10 \mu \mathrm{m} / \mathrm{s}\) at the time \(t=0 \mathrm{~s}\), and is then subject to the acceleration, \(a(t)=a_{0} \sin (2 \pi t / T)\), where \(a_{0}=1 \mu \mathrm{m} / \mathrm{s}^{2}\), and \(T=1 \mathrm{~ms}\). (a) Find the velocity of the bacterium as a function of time. (b) Find the position of the bacterium as a function of time. (c) Find the average velocity of the bacterium after a time \(t=10 T\).

As an expert archer you are able to fire off an arrow with a maximum velocity of \(50 \mathrm{~m} / \mathrm{s}\) when you pull the string a length of \(70 \mathrm{~cm}\). (a) If you assume that the acceleration of the arrow is constant from you release the arrow until it leaves the bow, what is the acceleration of the arrow?

Is is possible to go for a trip (in one dimension) where the total displacement is zero, but your average velocity is non-zero?
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