Ground Speed of Plane in Windy Conditions

[NeedHelpBro]

Homework Statement

A Jet is heading due east: its nose points towards the east direction, but its trajectory on the ground deviates from the east direction due to a sideways component of the wind. The plane is also climbing at the rate of 100 km/h (height increase per unit time). If the plane's airspeed is 520 km/h and there is a wind blowing 90 km/h to the northwest, what is the ground speed of the plane?

Homework Equations

√x²+y²+z²=a

The Attempt at a Solution

Is y=90j
z=100k

√x²+y²+z²=520 ?

And you solve for x?

 

[Ray Vickson]

Homework Statement

A Jet is heading due east: its nose points towards the east direction, but its trajectory on the ground deviates from the east direction due to a sideways component of the wind. The plane is also climbing at the rate of 100 km/h (height increase per unit time). If the plane's airspeed is 520 km/h and there is a wind blowing 90 km/h to the northwest, what is the ground speed of the plane?

Homework Equations

√x²+y²+z²=a

The Attempt at a Solution

Is y=90j
z=100k

√x²+y²+z²=520 ?

And you solve for x?

Try it and see!

BTW: your equations for y and z are wrong: y is a scalar and j is a vector, so you cannot have y = 90j, because a scalar cannot equal a vector. Your z-equation is wrong for the same reason.

 

[Orodruin]

Not only that, but you should also note that the wind is not orthogonal to the plane’s airspeed velocity. You need to find an expression for the total velocity in vector form.

 

[NeedHelpBro]

Try it and see!

BTW: your equations for y and z are wrong: y is a scalar and j is a vector, so you cannot have y = 90j, because a scalar cannot equal a vector. Your z-equation is wrong for the same reason.

Not only that, but you should also note that the wind is not orthogonal to the plane’s airspeed velocity. You need to find an expression for the total velocity in vector form.

I have tired my above equation and give me incorrect answer compare to answer provided.

How do find equation of the plane? I have draw what i think the question is asking. Is this correct?