Question

Heading straight towards the summit of Pike's Peak, an airplane of mass $12000kg$ flies over the plains of Kansas at nearly constant altitude $4.30km$ with constant velocity $175m/s$ west.
Does these value change us the airplane continues its motion along a straight line?

Answer 1

Given,

mass of airplane is $12000kg$

constant altitude $4.3km$

Constant velocity is $175m/s$

Let the positive $x$ direction is eastward,positive $y$ direction is northward and positive $z$ direction is vertically upward

$L$ is level of flight

$r=\left(4.3km\right)\hat{k}=(4.30\times {10}^{3}m)\hat{k}p=mv=12000kg(-175\hat{i}m/s)=-2.10\times {10}^{6}kg/m/sL=r\times p$

Substitute value of $r$ and $p$

$L=r\times pL=(4.3\times {10}^2\hat{k})\times (-2.10\times {10}^6\hat{i})L=-9.03\times {10}^{9}kg.m^2/s\hat{j}$

since, angular momentum is constant because level of airplane is constant Therefore,

airplane will not continue in straight line