Debbie wants to swim across the river and emerge exactly across the river from where she enters the water. But she sees that there is a current, and she knows if she swims straight across and ignores the current she will land downstream. Debbie knows that she can swim at 4 miles per hour in still water, and that the current is running at 3 miles per hour. In order to land exactly across from her starting place, she needs to angle herself to swim on a trajectory which is slightly upstream. What is the angle, rounded to the nearest degree, that she needs to achieve to land where she wants to?

Question

Zachery

Mathematics

20 April, 09:39

Debbie wants to swim across the river and emerge exactly across the river from where she enters the water. But she sees that there is a current, and she knows if she swims straight across and ignores the current she will land downstream. Debbie knows that she can swim at 4 miles per hour in still water, and that the current is running at 3 miles per hour. In order to land exactly across from her starting place, she needs to angle herself to swim on a trajectory which is slightly upstream. What is the angle, rounded to the nearest degree, that she needs to achieve to land where she wants to?

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Answers (1)

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Miley Foster · Answer 1

49°

Step-by-step explanation:

In the right triangle representing the sum of the various velocity vectors, the current represents the side opposite the angle, and the speed Debbie can swim represents the hypotenuse. The ratio Opposite/Hypotenuse is the sine of the angle, so we have ...

sin (α) = 3/4

α = arcsin (3/4) ≈ 48.6°

Debbie's swim direction needs to be about 49° upstream relative to the line she wants to follow.