Homework 1 - Scientific Notation and Vectors-Due January 23

1. Express the number 423 million in scientific notation with one number to left of decimal.

4.23 x 10^8

2. You measure the mass of a grain of sand as 1 milligram.

Express this in grams in scientific notation.

1.0 x 10^-3

Express this in kilograms using scientific notation

1.0 x 10^-6

Express this in pounds in scientific notation. (Look up the conversion factor)

2.21 x 10^-6

3. How many grains of sand are in an ordinary kid’s beach bucket?

First, how big is a grain of sand? (Estimate its volume)

Assuming that a grain of sand is spherical, to measure the volume of a grain of sand, we could use 𝑉 = 4

3𝜋𝑅3,

where V is volume and R is radius. Assuming that an average grain of sand has a radius of 0.5 millimeters,

that is 5.0 x 10^-4 m, V= 5.2 x 10^-10 𝑚3

Second, what is the volume of a bucket?

Assuming that a bucket is cylindrical, to measure volume of a bucket, we use 𝑉 = 𝜋𝑅2𝐻, where H is height.

Assuming that the radius of the bucket is 0.1 m, that is 1.0 x 10^-1 m, and height of the bucket is 0.3m,

V= 9.4 x 10^-3 𝑚3

How many grains?

Dividing the volume of bucket by volume of a grain of sand, we get 18076923 grains, which is 1.8 x 10^7

grains.

4. How many ping pong balls would it take to fill our classroom? Show how you arrive at your number.

Assuming a ping pong ball has a radius of 2.0 x 10^-2 m, a volume of ping pong ball is V= 3.351 x 10^-5 𝑚3.

Assuming the length of our classroom is about 5 meters, width is 10 meters, and height is 3 meters, thus volume of our classroom is 1.5 x 10^3 𝑚3.

Hence, 4477611.94 or 4.4 x 10^6 ping pong balls can fit into the classroom.

5. Using a ruler, your friend tells you he measured his height to be 1.8752 meters. How is he wrong?

Firstly, the length of a ruler is at most 30cm long, hence he could not possibly be using one ruler. Secondly, a ruler does not measure beyond 10^-3 m accuracy, and the figure stated was in 4 decimal places.

6. Using the Google Maps Mapping function, find a walking route from your college (closest street entrance) to the Bass library location shown on Google.

To make it easier for yourself, adjust the route so that all the legs are straight lines, or nearly straight

lines.

Take a screenshot of the route and include it in your homework.

Using the Google maps directions (to give you lengths) and the fact that north is directly upward, list each

vector in order that will take you from start to end. In other words, for each vector list the length of the

vector (in meters) and its angle relative to a cardinal direction(N-S-E-W). You may need to figure out a

way of estimating the angle of the vector relative to a cardinal direction.

Vector 1 (AB): 72m, Northwest 35°

Vector 2 (BC): 450m, Northeast 30°

Vector 3 (CD): 33m, Southeast 30°

Add up the lengths of all the vectors to give a total distance traveled in meters.

550m

Use a vector addition method of your choice to find the displacement, both magnitude (in meters) and

direction.

AB + BC + CD = AD

AD = (550m, 30°)

Estimate your average walking speed and then calculate how long it takes you to get from the start of

your route to the end.

Assuming I walk 1 m/s, I need 550 seconds, which is about 9 minutes.

Calculate your average velocity. Why is the magnitude of your average velocity different from your speed.

Velocity = Distance / time

=