Kinematics -- flying a plane in the wind to a destination

[Philly215]

Homework Statement

A plane is taking off from an airport directly west of the airport it wishes to touch down in. The plane in still air can travel with a constant speed of 730 km/h. If a wind is blowing constantly at 92 km/h [45° S of E], at what angle must the plane fly to compensate for the wind?

Homework Equations

Trig (sin, cos, tan) *no sin law*
V =d/t

The Attempt at a Solution

[/B]
730 km/h ÷ 92 km/h = 7.93 km/h
45/7.93= 5.67 ° [N of E]

* The answer for this question is 5.1° [N of E] and must be solved using resultant triangles, components and trig (no sin law). However, I am completely lost in solving this.

 

[berkeman]

Homework Statement

A plane is taking off from an airport directly west of the airport it wishes to touch down in. The plane in still air can travel with a constant speed of 730 km/h. If a wind is blowing constantly at 92 km/h [45° S of E], at what angle must the plane fly to compensate for the wind?

Homework Equations

Trig (sin, cos, tan) *no sin law*
V =d/t

The Attempt at a Solution

[/B]
730 km/h ÷ 92 km/h = 7.93 km/h
45/7.93= 5.67 ° [N of E]

* The answer for this question is 5.1° [N of E] and must be solved using resultant triangles, components and trig (no sin law). However, I am completely lost in solving this.

Welcome to the PF.

First, you should clarify what is meant by "[45° S of E]" -- does that mean the wind is coming from that direction, or blowing in that direction.

Next, draw a diagram showing the vectors of the plane's velocity (pointing left-to-right, angled either up or down), and the wind's velocity vector. When you place the vectors nose-to-tail (to add them), the resultant vector needs to point straight to the right (to the East).

Makes sense? Show us your sketch, please...

 

[gneill]

730 km/h ÷ 92 km/h = 7.93 km/h

You divided km/h by km/h and got a result with units of km/h? Shouldn't the units cancel?

45/7.93= 5.67 ° [N of E]

What was your thinking on the above step, dividing 45° by 7.93?

Did you draw a sketch of how the vectors should add? What direction should the resultant have?

Edit: Ah! berkeman got there ahead of me!

 

[Zygzak191]

Your mistake comes from assumption that x is proportional to sin(x) for degrees and such high value as 45°, try plugging the exact value of sin(45°). sin(x)~x for small angle values, but for x in radians.