Question

Anyone know how to do this one? The answers 81 km/h E60*N

Answer 1

Answer:

81 km/h W52°S

Explanation:

The bird's initial velocity is 25 km/h, 45° east of north.  The components of the velocity are:

aₓ = 25 sin 45

aᵧ = 25 cos 45

The bird's final velocity is 56 km/h, 35° west of south.  The components of the velocity are:

bₓ = -56 sin 35

bᵧ = -56 cos 35

The change in velocity is the final velocity minus the initial velocity.

cₓ = bₓ − aₓ

cₓ = -56 sin 35 − 25 sin 45

cₓ ≈ -49.8

cᵧ = bᵧ − aᵧ

cᵧ = -56 cos 35 − 25 cos 45

cᵧ ≈ -63.6

The magnitude is found using Pythagorean theorem:

c² = cₓ² + cᵧ²

c² = (-49.8)² + (-63.6)²

c ≈ 81 km/h

The direction is found using trigonometry:

θ = atan(cᵧ / cₓ)

θ = atan(-63.6 / -49.8)

θ ≈ 52°

The change in velocity is 81 km/h W52°S.