Question

a remote - controlled helicopter flew west at a constant velocity for 27.6 seconds. in that time, it flew 345 meters, and it was passed by a pigeon flying at 22 meters per second. what was the helicopters velocity? write your answer to the tenths place. meters per second to the west

Explanation:

Step1: Calculate the total distance flown by the helicopter

The formula for distance \(d = v\times t\). The pigeon's speed \(v_{pigeon}=22\) m/s. Let the helicopter's speed be \(v_{helicopter}\). The distance flown by the pigeon in \(t = 27.6\) s is \(d_{pigeon}=22\times27.6\)

$$d_{pigeon}=22\times27.6 = 607.2$$

The distance flown by the helicopter in \(t = 27.6\) s is \(d_{helicopter}=345\) m.

Step2: Use the relative - distance concept (assuming they start from the same point)

Since \(d_{pigeon}-d_{helicopter}=(v_{pigeon} - v_{helicopter})\times t\). We can rewrite it to find \(v_{helicopter}\):

$$v_{helicopter}=v_{pigeon}-\frac{d_{pigeon}-d_{helicopter}}{t}$$

Substitute \(d_{pigeon}=607.2\) m, \(d_{helicopter}=345\) m, and \(t = 27.6\) s

$$\frac{d_{pigeon}-d_{helicopter}}{t}=\frac{607.2 - 345}{27.6}=\frac{262.2}{27.6}=9.5$$

$$v_{helicopter}=22-9.5 = 12.5$$

Answer:

\(12.5\)