Consider an antelope being chased by a tiger. The antelope is running at a veloc

Question

Consider an antelope being chased by a tiger. The antelope is running at a velocity of 6.80 at an angle 12.5 E of S. The tiger is running at a velocity of 10.14 at an angle of 30.1 W of S. (Use East as positive x and North as postive y).
a)What are the x and y components of the antelope's velocity with respect to the ground?
b)What are the x and y components of the tiger's velocity with respect to the ground?
c)What are the x and y components of the velocity of the tiger with respect to the antelope?
d)What is the magnitude of the velocity of the tiger with respect to the antelope?

Explanation / Answer

use triangle trigonometry to find x and y components

a) it's east of south, so if you draw out the triangle you'll see that:

Vx = Vsin = 6.8sin(12.5)= 1.472m/s RIGHT
Vy = Vcos = 6.8cos(12.5) = 6.64m/s SOUTH

b) Vx = 10.14sin(30.1) = 5.085m/s LEFT
Vy = 10.14cos = 8.773m/s SOUTH

c) put them together (remember that the tiger is chasing the antelope, so from the antelope's point of view the tiger will be moving slower than from the ground's point of view)

Vx = 5.085m/s - 1.472 = 3.613 m/s
Vy = 8.773 - 6.64 = 2.133 m/s

d) pythagorean theorem
(3.6132 + 2.1332) = 4.20m/s

hope this helps a little

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