Make the given changes in the indicated examples of this section and then solve the resulting problems.

In Example 4, in the second line, change 27,000km/h to 27,100km/h.

Data from Example 4

A spacecraft maneuvers so that it may “capture” an already orbiting satellite that is 6000 km ahead. If the satellite is moving at 27,000 km/h and the spacecraft is moving at 29,500 km/h, how long will it take the spacecraft to reach the satellite?

First, we let t = the time for the spacecraft to reach the satellite. Then, using the fact that the spacecraft must go 6000 km farther in the same time, we draw the sketch in Fig. 1.20. Next, we use the formula distance = rate × time (d = rt). This leads to the following equation and solution.

29,500t = 6000 + 27000t

2500t = 6000

t = 2.00h

This means that it will take the spacecraft 2.400 h to reach the satellite. In 2.400 h, the spacecraft will travel 70,800 km, and the satellite will travel 64,800 km. 

We see that the solution checks with the statement of the problem.