Mathematics, 22.04.2020 04:26 estebanmff

A straight river flows east at a speed of 11 mi/h. A boater starts at the south shore of the river and wants to arrive at a point on the north shore of the river directly opposite the starting point. The motorboat has a speed of 22 mi/h relative to the water. In what direction should the boat be headed?

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The direction should the boat be headed is 60 degrees north 30 degrees west and this can be determined by using the trigonometric functions.

Given :

A straight river flows east at a speed of 11 mi/h. A boater starts at the south shore of the river and wants to arrive at a point on the north shore of the river directly opposite the starting point. The motorboat has a speed of 22 mi/h relative to the water.

The following steps can be used in order to determine the direction should the boat be headed:

Step 1 - The trigonometric function can be used in order to determine the direction should the boat be headed.

Step 2 - The mathematical expression of the cosine function is given by:

$\rm cos\theta=\dfrac{base}{hypotenuse}$

where $\theta$ is the direction should the boat be headed.

Step 3 - Now, substitute the known values in the above formula.

$\rm cos\theta=\dfrac{11}{22}$

Step 4 - Simplify the above expression.

$\rm cos\theta=\dfrac{1}{2}$

$\theta = 60^\circ$

Step 5 - So, the angle from the west axis is given by:

$90-60=30^\circ$

The direction should the boat be headed is 60 degrees north 30 degrees west.

For more information, refer to the link given below:

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Answer from: sullivanjakob

N 30 degree W

Step-by-step explanation:

We are given that

Speed of river flows=11 mi/h(East)

Speed of motorboat relative to water=22mi/h

We have to find the direction in which the boat should be headed.

Let direction of the boat = $\theta$

We know that

$Cos\theta=\frac{Base}{hypotenuse}$

Using the formula

$Cos\theta=\frac{11}{22}=\frac{1}{2}$

$Cos\theta=Cos60^{\circ}$

Because $Cos60^{\circ}=\frac{1}{2}$

$\theta=60^{\circ}$

Angle from the west axis= $90-60=30^{\circ}$ W

Hence, the direction of boat should be headed in N 30 degree W

Answer from: Quest

0 is its x and y coordinate

Line a b represents a proportional relationship. point a lies at 6, 4 as shown on the graph below :

Answer from: Quest

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to $\frac{1}{60} hr\\$

then mult. both sides by 75 we get the ratio

75 mi. to $\frac{75}{60} hr\\$

simplifying we get

75 mi. to $\frac{5}{4} hr$

or 1.25 hr.

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A straight river flows east at a speed of 11 mi/h. A boater starts at the south shore of the river a...

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