What is the relative velocity of the rabbit to the eagle?
Submitted : 20180614 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
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+V2^22*V1*V2*cos (90+45) = √79.2^2+30.1^22*79.2*30.1*0.707 = 102.71 km/h
heading = 90arctan (79.2*0.707/(79.2*0.707+30.1) = 57.0° NoW or 33.0° EoS
Rabbit is dead.


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