PROBLEM 3. A scientific capsule was carried aloft by a rocket and released at the peak of the rocket's trajectory. The rocket had an average vertical speed of 920 km an hour from liftoff to release of the capsule. The capsule made a controlled descent with an average vertical speed of 390 km an hour and landed 68 minutes after the rocket was launched. Find the maximum height reached by the rocket.
Solution: Let t be the time of ascent in hours. Then (68/60) - t is the time of descent, and since the distances of ascent and descent are equal,
920 t = 390 ([68/60] - t)
= 442 - 390 t
1310 t = 442
t= 0.34 h.
The maximum height = distance of ascent = (920 km/h) (0.34 h) = 310 km.
Italian scientist Galileo Galilei's introduction of the telescope for studying the heavens brought about a revolutionary change in astronomy. It is expected that a comparable leap in our ability to examine the universe will take place when the Hubble Space Telescope is launched into orbit by the Space Shuttle in 1986. Because the space telescope will be above Earth's atmosphere, it will be able to see much fainter objects than can now be seen by the best Earth-based telescopes. As we shall see in the next problem, this means that astronomers will soon be able to make observations and to compare them with the cosmological theories about the age and formation of the universe.