(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A plane traveling horizontally to the right at 100 m/s flies past a helicopter that is going straight up at 20 at 20 m/s. From the helicopter's perspective, the plane's direction and speed are:

a) Right and up, less than 100 m/s.

b) Right and up, 100 m/s.

c) Right and up, more than 100m/s.

d) Right and down, less than 100m/s.

e) Right and down, 100 m/s.

f) Right and down, more than 100 m/s.

2. Relevant equations

[itex]\vec{v} = \vec{v}' + \vec{V}[/itex]

[itex]\vec{v}[/itex] = velocity of the object in the helicopter's reference frame.

[itex]\vec{V}[/itex] = the relative velocity measured between two reference frames

[itex]\vec{v}'[/itex] = velocity of the plane relative to the helicopter's reference frame.

3. The attempt at a solution

Just a conceptual question that I do not have the answer to that appeared at the end of the chapter of my text. If the helicopter's reference frame is reference frame S, then the plane would have a vertical velocity component of -20 m/s and horizontal velocity component of 100 m/s. Using the equation:

[itex]\vec{v} = \vec{v}' + \vec{V}[/itex]

[itex]\vec{v} = (100\hat{i} - 20\hat{j}) m/s[/itex]

[itex]\vec{v} =\sqrt{(100^{2}) - (20^{2})}m/s \approx 102 m/s[/itex]

Therefore, relative to the helicopter's reference frame, the plane's velocity would be f) right and down, more than 100 m/s. Correct?

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# Homework Help: Relative motion problem.

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