Question

An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3015 feet and Plane B is just taking off. Plane A is gaining altitude at

30.25 feet per second and Plane B is gaining altitude at 80.5 feet per second.
How many seconds will pass before the planes
are at the same altitude?
seconds
What will their altitude be when they're at the
same altitude?
feet

Answer 1

a) Altitude of Plane A (in meters) = 3015+24t

Altitude of Plane B (in meters) = 80.5t

b) 3015 + 24t = 80.5t

Explanation:

a) We have that Plane A has an altitude of 3015m, and is gaining altitude at 30.25m/s.

Plane B has an altitude of 0m and is gaining altitude at 80.5 m/s.

To know the altitudes of Planes A and B we have to add the altitude they have plus the product of the altitude they are gaining and the time in seconds:

An expression for this would be:

Altitude of Plane = x + yt

where:

x is the altitude that they start with, in meters

y is the gaining altitude in m/s

t is the time in seconds

We substitute the values for plane A

Altitude of plane A = 3015m + 30.25m/s x t

We substitute the values for plane B

Altitude of Plane B = 0m + 80.5m/s x t

Altitude of Plane B = 80.5m/s x t

b) An equation to show that the two planes are at the same altitude we have to equalize the two expressions of the planes:

Altitude of Plane A = Altitude of Plane B

We can change this to:

3015m + 30.25m/s x t = 80.2m/s x t

This is the expression.

(To know how much time will it take them to have the same altitude we just have to solve for t:

3015 + 30.25t = 80.5t

3015 = 80.5t - 30.25t

3015 = 50.25t

3015/50.25 = t

t = 60 seconds

And the planes will have an altitude of:

Altitude of plane A = 3015 + 30.25 x 60

Altitude of Plane A = 4830 m

Altitude of Plane B = 80.5 x 60

Altitude of Plane B = 4830)

Answer 2

Let's denote the time in seconds when the planes are at the same altitude as t. At time t, the altitude of Plane A and Plane B will be the same. We can set up two equations based on the given information:

Altitude of Plane A = 3015 + 30.25t
Altitude of Plane B = 0 + 80.5t (Plane B starts at an altitude of 0)

Now, we can set these equations equal to each other to find the time when both planes are at the same altitude:

3015 + 30.25t = 80.5t

Now, let's solve for t:

3015 = 50.25t
t ≈ 60 seconds

So, it will take about 60 seconds for both planes to be at the same altitude.

Now let's find the altitude at which they will be at the same height:

Altitude of Plane A = 3015 + 30.25 * 60 ≈ 4815 feet
Altitude of Plane B = 80.5 * 60 ≈ 4830 feet

Since these values are close and we rounded the time, we can say that the altitude at which both planes will be at the same height is approximately 4815-4830 feet.