A river flows due south at 1.4 mi/h. In what direction should the swimmer head, at a velocity of 3 mi/h, in order to arrive at a landing point due east of his starting point? (Round your answer to one decimal place.)

Solution:

It is that a river is flowing in the south direction with a speed of 1.4 mi/h.

A swimmer wishes to cross the river in a horizontal direction so that he lands at a point which is due east of his starting point.

The speed of the swimmer is = 3 mi/h

Therefore he has to swim in such a direction that his resultant is in the direction east to his starting point.

Let this angle be θ.

Therefore, from the figure,

Therefore, the swimmer has to swim in the northeast direction making an angle of (90+27.4) = 117.4° with the direction of flow of river (i.e. south).  

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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a 90 degree rotation across the the origin followed by a reflection across the x-axis.

step-by-step explanation: