QuestionAircraft A flies East at $340 \mathrm{kt}$ , while Aircraft B is $210 \mathrm{NM}$ ahead at $280 \mathrm{kt}$ . Find the distance B travels when A catches up.

Studdy Solution

STEP 1

Assumptions1. Aircraft A is flying at a speed of340 NM/hr. Aircraft B is flying at a speed of280 NM/hr3. Aircraft B is initially210 NM ahead of Aircraft A4. Both aircraft are flying in the same direction5. We need to find the distance travelled by Aircraft B when Aircraft A catches up to it

STEP 2

First, we need to find the relative speed of Aircraft A with respect to Aircraft B. This is the speed at which Aircraft A is catching up to Aircraft B. We can calculate this by subtracting the speed of Aircraft B from the speed of Aircraft A.
$Relative\, speed = Speed\, of\, Aircraft\, A - Speed\, of\, Aircraft\, B$

STEP 3

Now, plug in the given values for the speeds of Aircraft A and B to calculate the relative speed.
$Relative\, speed =340\, NM/hr -280\, NM/hr$

STEP 4

Calculate the relative speed.
$Relative\, speed =340\, NM/hr -280\, NM/hr =60\, NM/hr$

STEP 5

Now that we have the relative speed, we can find the time it takes for Aircraft A to catch up to Aircraft B. This is the initial distance between the two aircraft divided by the relative speed.
$Time = Initial\, distance / Relative\, speed$

STEP 6

Plug in the values for the initial distance and the relative speed to calculate the time.
$Time =210\, NM /60\, NM/hr$

STEP 7

Calculate the time it takes for Aircraft A to catch up to Aircraft B.
$Time =210\, NM /60\, NM/hr =3.5\, hr$

STEP 8

Now that we have the time it takes for Aircraft A to catch up to Aircraft B, we can find the distance travelled by Aircraft B during this time. This is the speed of Aircraft B multiplied by the time.
$Distance\, travelled\, by\, B = Speed\, of\, Aircraft\, B \\times Time$

STEP 9

Plug in the values for the speed of Aircraft B and the time to calculate the distance travelled by B.
$Distance\, travelled\, by\, B =280\, NM/hr \\times3.5\, hr$

STEP 10

Calculate the distance travelled by Aircraft B.
$Distance\, travelled\, by\, B =280\, NM/hr \\times3.5\, hr =980\, NM$ Aircraft B will have travelled980 NM when Aircraft A catches up to it.

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