Forces and Motion

Miles and Kilometers

Here is a scientific secret.

Scientists don’t think in miles, feet or inches. All scientists on Earth use metric units such as kilometers, centimeters and millimeters. The reason is that metric units are MUCH easier to convert from one to another because all are multiples of 10. For example, it is much easier to convert kilometers to meters (1 km  = 1000 m) than miles to feet (1 mile = 5280 ft). To avoid these conversion woes, from now on in this book, all measurements will be in metric units. Here are some conversions. A complete list is in the Appendix.

Equals

1 mile

1 ft

1 in

1 km

1 m

1 cm

1 mm

1.61 km

0.30 m

2.54 cm

0.62 mi

3.28 ft

0.40 in

0.04 in

=

=

=

=

=

=

=

Speed and Velocity

Solve This!

Equation 1 works for any set of distances and times, even if you want to plan a trip to Mars, seen here in an image taken with the Hubble Space Telescope. To travel to Mars, NASA selects a trajectory that uses the least amount of rocket fuel (rocket fuel is expensive). To do this, we cannot travel in a straight line between Earth and Mars (because the gravity of Earth and Sun bends trajectories) but instead in an orbital path around the sun called a Hohmann Transfer Orbit. This takes approximately 8 1/2 months, and if done correctly the rocket and Mars arrive at the same location simultaneously.

Hohmann Transfer TrajectoryLaunch Animation

Time to travel to Mars:

8½ months or about 260 days

Distance Traveled:

Average Speed:

mph

Here is how to do the problem:
v = d/t = 4.0 x 108 miles/(260 days x 24 hrs/day)

v= 4.0 x 108 miles/6.1 x 103 hrs = 0.66 x 105 m/h = 6.6 x 104 m/h = 66,000 m/h
The only thing difficult here is converting 8.5 months to hours.

Using the metric units for the Mars problem:

Travel time = 260 days

Distance traveled: 640 million km

(converted from miles with 1 miles = 1.6 km)

v = d/t = 640,000,000 km/260 days = 2,500,000 km/day

v = 103,000 km/hr

Screamingly fast!