Webpage title: Relative Motion Problem: Plane and Helicopter Velocity

[-Dragoon-]

Homework Statement

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.

Homework Equations

$\vec{v} = \vec{v}' + \vec{V}$
$\vec{v}$ = velocity of the object in the helicopter's reference frame.
$\vec{V}$ = the relative velocity measured between two reference frames
$\vec{v}'$ = velocity of the plane relative to the helicopter's reference frame.

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:
$\vec{v} = \vec{v}' + \vec{V}$
$\vec{v} = (100\hat{i} - 20\hat{j}) m/s$
$\vec{v} =\sqrt{(100^{2}) - (20^{2})}m/s \approx 102 m/s$
Therefore, relative to the helicopter's reference frame, the plane's velocity would be f) right and down, more than 100 m/s. Correct?

 

[Ignea_unda]

Bingo!

 

[-Dragoon-]

Bingo!

Great. Thank you.