Imagine you are in an airplane that is slowly spiraling in for a landing. The po

Question

Imagine you are in an airplane that is slowly spiraling in for a landing. The position vector of the airplane as described by someone on the ground is given by

When the airplane lands, how many complete rotations and fractions there of has it made? Now sitting in your seat facing the front of the plane, you decide to define mutually orthogonal unit vectors with you at their origin. The Direction when you look striaght ahead is your 'x-direction' and the direction of your left shoulder is your 'y-direction'. Finally, your 'z-direction' is perpendicular to these two. Write explicit expressions for 'your' unit vectors as described by someone on the ground. In your frame of reference, write Newton's second law.

Explanation / Answer

Time period of one rotation, To = 2/o

The time it takes the airplane to land, tland = Ho/vo

So the number of rotations are, n = tland/To = Hoo/2vo

At t = tland = Ho/vo ,

Rp = o[cos(oHo/vo)x - sin(oHo/vo)y]

So, the unit vectors of my position as described by someone on the ground is,

rp = cos(oHo/vo)x - sin(oHo/vo)y

In my reference frame, newton's second law is,

Fnet = F + Ffic = (mo2oy - mgz) + (-mo2oy + mgz) = ma = 0

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.