 ×     #### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
```
An aeroplane has to go from a point a to another point b 500 km away due 30 degree East of north wind is blowing due north at the speed of 20 metre per second the steering speed of plane is 150 metre per second Find the direction in which the pilot should head the pain to reach the point p Find the time taken by the plane to go from a to b Kindly use sine formula.

```
one year ago

```							Wind travels at a Speed =u=20m/sAeroplane travels at a Speed  =v=150m/sTo reach the point B, The pilot should travel along AB.Let us assume that θ be the angle at which the plane heads towards east of line AB.so angle between two velocities is θ+30°tanθ°=usin(θ+30)/(v+ucos(θ+30))sinθ°/cosθ°=usin(θ+30)/(v+ucos(θ+30))By cross multiplying we getsinθ°(v+ucos(θ+30))=cosθusin(θ+30)sinθ° [v+ucosθcos30° - usinθsin30)]=ucosθ°sinθ°cos30°+ucosθ°cosθ°sin30Since Cos(A+B)=cosAcosB-SinASinB]Sin(A+B)=sinACosB+cosAsin BVsinθ°+ucosθ°sinθ°√3/2-usin²θ1/2=ucosθ°sinθ°√3/2+ucos²θ°1/2on solving the above equation,we getvsinθ°-u/2sin²θ=u/2cos²θVsinθ°=(u/2)[cos²θ+sin²θ]V sinθ°=u/2 [ ∵cos²θ+sin²θ=1]sinθ=u/2v=20/2x150=20/300=1/15θ=sin⁻¹[1/15]=sin⁻¹[0.066]
```
one year ago
```							The vector diagram for various velocities is shown.Vector AC gives velocity of aero plane relative to quiet air.Vector CB gives velocity of wind(air) relative to ground.Vector AB gives velocity of plane relative to ground.Using law of sines for triangle,(150/sin 30 degree) = (20/sin theta).Therefore, sin( theta)=(20/300)=(1/15). Then,Theta=sin^-1(1/15)=3.8 degree.Angle NAC=33.8 degree.The pilot should head the plane in the direction 33.8 degree east of north.
```
one year ago
Think You Can Provide A Better Answer ?

## Other Related Questions on General Physics

View all Questions »  ### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  ### Course Features

• 18 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions