I was wondering if you guys can help me with this question

An airplance is traveling 835 km/h in a direction 41.5 degrees west of north.
part a) find the component of the velocity in the northerly direction
part b) find the same but in the westerly direction
part c) how far north has the plane traveled after 2.40 h ?
part d) how far west has the plane traveled after 2.40 h

i already find out the answers to the first two which is for north is 625 and for west is 553 km/h but I am getting the wrong answer for the last two. please help me and thank you

SKETCH THE PROBLEM on a graph!!!

a
835 cos 41.5

b
835 sin 41.5

c
distance = speed * time
2.4 * 835 cos 41.5

d
2.4 * 835 * sin 41.5

Sure, I can help you with that. Let's break down each part of the question step-by-step:

Part a) To find the component of the velocity in the northerly direction, we need to determine the vertical component of the airplane's velocity. We can use the formula:

Vertical Component = Velocity * sin(angle)

Given:
Velocity = 835 km/h
Angle = 41.5 degrees west of north

Using the given values, we can calculate the vertical component:

Vertical Component = 835 km/h * sin(41.5 degrees)
Vertical Component = 625 km/h

Therefore, the component of the velocity in the northerly direction is 625 km/h.

Part b) To find the component of the velocity in the westerly direction, we need to determine the horizontal component of the airplane's velocity. We can use the formula:

Horizontal Component = Velocity * cos(angle)

Given:
Velocity = 835 km/h
Angle = 41.5 degrees west of north

Using the given values, we can calculate the horizontal component:

Horizontal Component = 835 km/h * cos(41.5 degrees)
Horizontal Component = 553 km/h

Therefore, the component of the velocity in the westerly direction is 553 km/h.

Part c) To calculate how far north the plane has traveled after 2.40 hours, we can use the formula:

Distance = Velocity * Time

Given:
Velocity = 625 km/h (component of the velocity in the northerly direction)
Time = 2.40 hours

Using the given values, we can calculate the distance traveled:

Distance = 625 km/h * 2.40 hours
Distance = 1500 km

Therefore, the plane has traveled 1500 km north after 2.40 hours.

Part d) To calculate how far west the plane has traveled after 2.40 hours, we can use the formula:

Distance = Velocity * Time

Given:
Velocity = 553 km/h (component of the velocity in the westerly direction)
Time = 2.40 hours

Using the given values, we can calculate the distance traveled:

Distance = 553 km/h * 2.40 hours
Distance = 1327.2 km

Therefore, the plane has traveled approximately 1327.2 km west after 2.40 hours.

Please let me know if you need any further assistance!

To solve parts c) and d), you need to use the information given and apply the concept of velocity and time to find displacement.

Part c) How far north has the plane traveled after 2.40 h?

To answer this question, you need to calculate the distance the plane traveled in the northward direction in 2.40 hours.

First, recall that velocity is a vector quantity with both magnitude and direction. In this case, the velocity of the plane is 835 km/h in a direction 41.5 degrees west of north.

To find the component of velocity in the northerly direction, you can use trigonometry. The velocity vector can be split into its northward and westward components.

The northward component (Vn) can be found using the formula:
Vn = V × sin(θ)
where V is the magnitude of the velocity (835 km/h) and θ is the angle of motion (41.5 degrees west of north).

To calculate Vn:
Vn = 835 km/h × sin(41.5 degrees)
Vn ≈ 835 km/h × 0.638
Vn ≈ 532.33 km/h

Now that you have the northward component of velocity, you can calculate the distance traveled in the northward direction by multiplying it with the time (2.40 h):
Distance north = Vn × time
Distance north = 532.33 km/h × 2.40 h
Distance north ≈ 1277.59 km

Therefore, after 2.40 hours, the plane would have traveled approximately 1277.59 km north.

Part d) How far west has the plane traveled after 2.40 h?

Similarly, to find the distance traveled in the westerly direction, you need to calculate the westward component of velocity (Vw).

The westward component (Vw) can be found using the same formula as before:
Vw = V × cos(θ)
where V is the magnitude of the velocity (835 km/h) and θ is the angle of motion (41.5 degrees west of north).

To calculate Vw:
Vw = 835 km/h × cos(41.5 degrees)
Vw ≈ 835 km/h × 0.770
Vw ≈ 643.34 km/h

Now, you can find the distance traveled in the westerly direction by multiplying Vw with the time (2.40 h):
Distance west = Vw × time
Distance west = 643.34 km/h × 2.40 h
Distance west ≈ 1544.02 km

Therefore, after 2.40 hours, the plane would have traveled approximately 1544.02 km west.

Please note that the values obtained may differ slightly due to rounding in intermediate steps.