A space shuttle 200 miles above the earth is orbiting the earth once every 12 hours. How far does the shuttle travel in 1 hour? (Assume the radius of the earth is 4,000 miles.) Give your answer as both an exact value and an approximation to three significant digits (see the figure below).
+130516 Edit ....[ Sorry..... I hit the wrong buttons on the calculator before !!!]
The distance traveled in one hour is given by:
d= r[theta] = 4200 [ 2pi/12] = 4200[pi / 6] = about 2199.1148575128552669 mi/hr =
2199.115 mi/hr to 3 sig. decimal digits
+26400 A space shuttle 200 miles above the earth is orbiting the earth once every 12 hours. How far does the shuttle travel in 1 hour? (Assume the radius of the earth is 4,000 miles.) Give your answer as both an exact value and an approximation to three significant digits
orbit = \(2\pi \cdot (4000+200)\ \text{miles} = 2\pi\cdot 4200 \ \text{miles}\)
velocity = \(\frac{orbit}{12 \ \text{hours} } = \frac{ 2\pi \cdot 4200\ \text{miles} } {12 \ \text{hours} } = \frac{ \pi \cdot 4200\ \text{miles} } { 6 \ \text{hours} } = 700\pi \cdot \frac{ \text{miles} } { \text{hour} } \)
The shuttle travel in 1 hour
\(700\cdot\pi \ \text{miles} = 2199.11485751\ \text{miles} \approx2199.115 \ \text{miles} \)
