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

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

Step-by-step 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=√((693)^2+(798)^2+2*693*798\cos37)`

`v=1414.3\ mph`

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