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What is the relative velocity of the rabbit to the eagle?

Author :

Submitted : 2018-06-14 06:02:39    Popularity:     

Tags: velocity  relative  eagle  rabbit  

An eagle flies towards the north west with a speed of 79.2 km/h. A rabbit on the ground sees the eagle and runs towards the south at a speed of 30.1 km/h. a) What is the relative velocity of the rabbit to the eagle? (magnitude) b) Direction: at an angle

Answers:

My answer is same as that of @Willgelmo. You are given two sides and one angle in a triangle, and you need to find the third side. I used the law of cosines in the equation below and substituted -->
a² = b² + c² – 2bc cosA
= 79.2² + 30.1² - [2 * 30.1 * 79.2 * cos (135)] So, a = √(10549.51288) = 102.7108 km/h
The direction is South of east.

F. Viete theorem (aka cosine theorem) shall apply :
V rel = √V1^2+V2^2-2*V1*V2*cos (90+45) = √79.2^2+30.1^2-2*79.2*30.1*-0.707 = 102.71 km/h
heading = 90-arctan (79.2*0.707/(79.2*0.707+30.1) = 57.0° NoW or 33.0° EoS

Rabbit is dead.



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