Question

A motorboat sets out in the direction N 77 degrees 48 minutes E. THe speed of the boat in still water is 31.7 mph. If the current is flowing directly south, and the actual direction of the motorboat is due east, find the speed of the current and the actual speed of the motorboat

Answer 1

Answer:

7.09 mph

30.87 mph

Step-by-step explanation:

We are given that

$\theta=77^{\circ} 48'=77+\frac{48}{60}=77.8^{\circ}$

1 degree=60 minute

The speed of boat in still water=v=31.7mph

We have to find the speed of the current and the actual speed of the motorboat.

$\theta'=90-77.8=`2.92^{\circ}$

Speed of the current=$vsin\theta'$

Speed of the current=$31.7sin12.92=7.09 mph$

Actual speed of the motorboat=$vcos\theta'=31.7cos12.92=30.87mph$

Answer 2

The speed of the current is 70.9 mph.

The actual speed of the motorboat is 30.87 mph.

Calculation of the speed:

Since it is mentioned that A motorboat sets out in the direction N 77 degrees 48 minutes E

So,

= 77 + 48/60

= 77.8 degrees

Also,

1 degree = 60 minute

Also, The speed of the boat in still water = v=31.7mph

So, here the speed of the current is

= 31.7  sin 12.92

= 7.09 mph

And, the actual speed of the motorboat is

= 31.7 cos(90-77.8)

= 31.7 cos2.92

= 30.87 mph

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