Ground Speed of Plane in Windy Conditions

AI Thread Summary
The discussion revolves around calculating the ground speed of a jet heading east while climbing, affected by a northwest wind. The plane's airspeed is given as 520 km/h, with a climbing rate of 100 km/h and a wind speed of 90 km/h. Participants highlight the need to express the velocities in vector form, noting that the wind's direction is not orthogonal to the plane's trajectory. There are corrections regarding the use of scalars and vectors in equations, indicating that the initial attempts at solving the problem were flawed. The conversation emphasizes the importance of accurately representing the components of velocity to find the correct ground speed.
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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?
 
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NeedHelpBro said:

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.
 
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.
 
Ray Vickson said:
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 said:
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?

upload_2018-4-1_19-9-47.png
 

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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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