Respuesta :
Answer
given,
taking x-direction at west and y-direction as north
Wind is moving from east to west
x = 40 Km/h, y = 0 Km/h
bird has to fly opposite to the wind
speed of wind, x = -40 Km/h
a) angle of bird
[tex]\theta = sin^{-1}(\dfrac{40}{100})[/tex]
θ = 23.58° South of West
b) Speed of the bird = 100 Km/h
Speed of bird north to south = 100 cos 23.58°
= 91.65 Km/h
time taken to travel 500 Km
[tex]t = \dfrac{500}{91.65}[/tex]
t = 5.45 hr
time to travel 500 Km from North to south is equal to 5.45 hr.
The velocity of the bird can be directed such that the resultant velocity of
the bird and the wind will be in the southward direction.
(a) To travel directly southward relative to the ground, the bird should head
to an angle direction of approximately South 23.58° East.
(b) The time it would take the bird to travel 500 km from North to South is
approximately 5.46 hours.
Reason:
component of the velocity are;
The magnitude of the velocity of the bird = 100 km/h
Direction of the bird = North-South direction
Magnitude of the velocity of the wind = 40-km/h
Direction of the wind = East-west direction
(a) The component vector of the two velocities are;
Velocity of bird, v[tex]_{bird}[/tex] = -100·j
Velocity of wind, v[tex]_{wind}[/tex] = 40·i
The direction of the velocity of the bird will be southward if it has a
component of velocity to accommodate the velocity of the wind.
Let θ represent the angle of the direction of the bird relative to the
negative x-axis, we have;
-100 × cos(θ) = -40·i
- [tex]\theta = arcos \left(\dfrac{-40}{-100} \right) \approx 66.42^{\circ}[/tex]
θ ≈ 66.42° in the the third quadrat, given that both the y, and x, values are
negative.
In the South-West direction, the angle is therefore; 90 - 66.42 ≈ 23.58°
Therefore, the bird should fly in the direction south 23.58° east to fly
directly southward relative to the ground
(b) The component of the birds velocity southward when moving in the
new direction, [tex]v_y[/tex], is given as follows;
[tex]v_y[/tex] = 100 × sin(θ)
Therefore;
Southward velocity, [tex]v_y[/tex] = 100 × sin(66.42°)
The time, t, it takes to travel 500 km, is given as follows;
[tex]t = \dfrac{500 \, km}{100 \, km/hr \times sin(66.42^{\circ})} \approx 5.46 \, hr[/tex]
The time it would take the bird to travel 500 km from North to South, t ≈
5.46 hours
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