Question

I am stuck on this question D: please help!!

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Scuba divers count fin strokes to estimate
the distance they have travelled under
water. Felipe uses this method and a
compass to swim 300 m north from the
dive boat. He then turns right 120° and
swims 400 m. How far from the boat is he,
to the nearest metre? In what direction
must Felipe swim to return to the boat?

Answer 1

Scuba divers use fin strokes to estimate distance traveled underwater. Felipe swims north from the dive boat and then turns right. To find his distance from the boat, calculate the total displacement using vector addition. To find the direction back to the boat, use vector subtraction.

Step-by-step explanation:

Scuba Diving and Distance Calculation

Scuba divers use the method of counting fin strokes to estimate the distance they have traveled underwater. In this question, Felipe swims 300 m north from the dive boat and then turns right 120° and swims 400 m. To find out how far he is from the boat, we can use the concept of vector addition. The total displacement is the sum of the individual displacements:

Displacement from boat = Displacement north + Displacement to the right

To find the displacement north, we can use the given distance of 300 m. Since it is north, the vertical component of displacement is positive:

Displacement north = 300 m

To find the displacement to the right, we can use the given distance of 400 m and the given angle of 120°. We can use trigonometry to find the horizontal component of displacement:

Horizontal component = 400 m * cos(120°)

Now we can calculate the total displacement:

Total displacement = Displacement north + Displacement to the right

To find the direction Felipe must swim to return to the boat, we can use the concept of vector subtraction. The direction is the opposite of the direction of the total displacement:

Direction back to the boat = 180° - (angle of total displacement)

Answer 2

She's approximately 361 m from the boat. Since she turned 120 degrees and swimmed for 400 m, she went back a vertical distance of 400*1/2=200 m, so she's 300-200=100 m away vertically. Horizontally, her distance to the boat is 400*cos30=200*\sqrt(3) meters, and using pythagoren's theorem, the distance to the boat is 100*\sqrt(13)=361m.  Arctan (200*\sqrt(3)/100)=74 degrees, so she has to swim to south from west 90-74=16 degrees.