A small plane is 150km south of the equator. The plane is flying at 220km/h at a heading of 30 degrees to the west of north. In how many minutes will the plane cross the equator?

Question

A small plane is 150km south of the equator. The plane is flying at 220km/h at a heading of 30 degrees to the west of north. In how many minutes will the plane cross the equator?

Answer 1

North speed = 220 cos 30 = 190.5 km/60 min

= 3.18 km/min

150 km /3.18 km/m = 47.2 minites

Answer 2

To find out how many minutes it will take for the plane to cross the equator, we need to determine its rate of northward travel.

First, we can find the northward component of the plane's velocity by multiplying its speed (220 km/h) by the sine of the angle between its heading and the north direction. In this case, the angle is 30 degrees west of north, so the angle with respect to the north direction would be 60 degrees.

The formula for the northward component of velocity is:

Northward Velocity = Velocity * sin(Angle)

Thus, the northward component of the velocity would be:

Northward Velocity = 220 km/h * sin(60°)

To calculate this, we need to convert the angle from degrees to radians, as trigonometric functions typically operate in radians. The conversion factor is π/180.

So, the northward component of the velocity is:

Northward Velocity = 220 km/h * sin(60° * π/180)

Next, we need to calculate the time it takes for the plane to cross the equator. Since we have the distance (150 km) and the northward velocity, we can use the formula:

Time = Distance / Velocity

In this case, the time will be in hours. However, since we want the answer in minutes, we can convert it by multiplying by 60.

Time (in minutes) = Time (in hours) * 60

Now, let's plug in the values and calculate the time it takes for the plane to cross the equator.

First, we calculate the northward velocity:

Northward Velocity = 220 km/h * sin(60° * π/180)
Northward Velocity ≈ 220 km/h * 0.866
Northward Velocity ≈ 190.52 km/h

Next, we calculate the time it takes to cross the equator:

Time (in hours) = 150 km / 190.52 km/h
Time (in hours) ≈ 0.787 hours

Time (in minutes) = 0.787 hours * 60
Time (in minutes) ≈ 47.22 minutes

Therefore, it will take approximately 47.22 minutes for the plane to cross the equator.