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Page 90
CA.7- i:s
Application of Vectors to Velocity and Acceleration
1.
The Viking 2 Orbiter~ which surveyed Mars from September 1975 to August
1976, moved in an elliptical orbit around Mars. The semi-major axis of this orbit
was 22, 030 lan. Show the orbital period was about 1655 minutes.
Hint: The gravity of Mars holds the Orbiter in its elliptical orbit about Mars in
exactly the same way that the sun holds each planet in its orbit about the sun.
Assume the following constant values:
Newton's Constant ofUniversal Gravitation G = 6.6720x 1O-1J Nm 2 kg- 2
When using this constant, all distances must be expressed in meters, mass
in kilograms and time in seconds.
Mass of Mars is 6.418 x 1023 kg
2.
•
In July 1965, the USSR launched Proton I, weighing 12,200 kg (at launch), with a
perigee (minimum distance above earth) of 183 Ian and an apogee of 589 Ian.
The period of the orbit ofProton I was 92.25 minutes. Use this information in
conjunction with any relevant information presented in lecture about orbits of
objects (determined by the force ofgravitational attraction) to compute the radius
ofthe earth. Give your answer in kilometers. Then go look up the radius of the
earth (site the reference, please) and compare your calculated result with this
value. Note:
Earth's Mass = 5.975 X 1024 kg
•
3.
A particle moves so that its derivative of its position vector is always orthogonal
to the position vector. Show that the particle moves on a circle.
4."
Determine the maximum height and range of a projectile fired 1.5 m above the
ground with an initial velocity of 100 mls at an angle of30 degrees above the
horizontal.
5.
A projectile is fired from ground level at an angle of 8 degrees with the
horizontal. Find the smallest velocity necessary if the projectile is to have a range
of 50 meters.
149
Page 91
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