Question

The speed of the plane relative to the air (called the air speed) as measured by instruments aboard the plane is 310km/hour . In which direction should the pilot head?
1. The wind is blowing southward at 75.0km/hour . In what frame of reference is this speed measured?

a. The speed is measured relative to the plane.
b. The speed is measured relative to the air.
c. The speed is measured relative to the ground.

2. An airplane pilot wishes to fly directly westward. According to the weather bureau, a wind of 75.0km/hour is blowing southward. The speed of the plane relative to the air (called the air speed) as measured by instruments aboard the plane is 310km/hour . In which direction should the pilot head?

3. In this particular problem, you can compare the speed of the plane relative to the ground (the ground speed) to known quantities to evaluate the reasonableness of your answer. Find the ground speed of the plane, vP/G.

Answer 1

Answer:

a)  correct answer is C , b) 14º  from the west to the north, c)   v_{1g} = 300.79 km / h

Explanation:

This is a relative speed exercise using the addition of speeds.

1) when it is not specified regarding what is being measured, the medicine is carried out with respect to the Z Earth, therefore the correct answer is C

2 and 3) In this case we must compose the speed using the Pythagorean Theorem.

     $v_{1a}$² = $v_{1g}$² + $v_{ag}$²

where v_{1a} is the speed of the airplane with respect to the air, v_{1g} airplane speed with respect to the Earth, v_{ag} air speed with respect to the Earth

in this case let's clear the speed of the airplane with respect to the Earth

  v_{1g} = √(v_{1a}² - v_{ag}²)

 v_{1g} = √ (310² - 75²)

 v_{1g} = 300.79 km / h

we find the direction of the airplane using trigonometry

   sin θ = v_{ag} / v_{1a}

   θ = sin⁻¹ (v_{ag} /v_{1a})

   θ = sin⁻¹ (75/310)

   θ= 14º

the pilot must direct the aircraft at an angle of 14º from the west to the north