Question

A jet airliner moving initially at 693 mph (with respect to the ground) to the east moves into a region where the wind is blowing at 798 mph in a direction 37◦ north of east. What is the new speed of the aircraft with respect to the ground? Answer in units of mph.

Answer 1

Answer:

The new speed of the aircraft with respect to the ground is 1414.3 mph.

Explanation:

Given that,

Angle = 37°

Velocity of jet airliner = 693 mph

Velocity of wind = 798 mph

We know that,

The new velocity of the aircraft with respect to the ground

$v=v_{a}+v_{w}$

We need to calculate the new speed of the aircraft with respect to the ground

Using formula for velocity

$v=\sqrt{(v_{a})^2+(v_{w})^2+2v_{a}v_{w}\cos\theta}$

Put the value into the formula

$v=\sqrt{(693)^2+(798)^2+2\times693\times798\cos37}$

$v=1414.3\ mph$

Hence, The new speed of the aircraft with respect to the ground is 1414.3 mph.