Question

A novice pilot sets a plane’s controls, thinking the plane will fly at 2.50 × 102 km/h to the north. if the wind blows at 75 km/h toward the southeast, what is the plane’s resultant velocity? use graphical techniques.

Answer 1

Velocity of plane is given as

$v_1 = 2.50 * 10^2 km/h$ towards north

$v_2 = 75 km/h$ towards south east

we can write the two velocity in vector form

$v_1 = 2.50 * 10^2 \hat j$

$v_2 = 75 cos45 \hat i - 75 sin45 \hat j$

now the net velocity will be given as

$v_{net} = v_1 + v_2$

$v_{net} = 250\hat j + 53.03 \hat i - 53.03 \hat j$

$v_{net} = 53.03\hat i + 196.97 \hat j$

so the resultant velocity will be given as

$v_{net} = \sqrt{53.03^2 + 196.97^2}$

$v_{net} = 203.98 m/s$

and the angle of velocity will be

$\theta = tan^{-1}\frac{v_y}{v_x}$

$\theta = tan^{-1}\frac{196.97}{53.03} = 74.9 degree$