A plane files from base camp to lake A, 260 km away in the direction 20.0 degree

Question

A plane files from base camp to lake A, 260 km away in the direction 20.0 degree north of east. After dropping att supplies it files to lake B, which is 240 km at 30.0 degree west at north from lake A. Graphically determine the distance and direction from lake B to the base camp. Distance km Direction degree --Direction-- A vector has an x component of -27.0 units and a y component of 39.4 units. Find the magnitude and direction of this vector. magnitude unit(s) direction degree counterclockwise from the +x axis A man pushing a map across a floor causes it to undergo two displacements. The first has a magnitude of 1.52 cm and makes an angle of 110 degree with the positive x axis. The resultant displacement has a magnitude of 141 cm and is directed at an angle of 30.0 degree to the positive x axis. Find the magnitude and direction of the second displacement. magnitude cm direction degree (counterclockwise from the positive x-axis)

Explanation / Answer

7. Let the East be the x-axis and the North be the y-axis.

First determine the x- and y- distances to lake A from Base Camp.

given that, base camp to lake A is 260km at a direction of 20degree north of east.

x1 = 260cos(20°)=244.32

y1 = 260sin(20°)=88.93

now given lake A to lake B is 240km at a direction of 30degree west of north

so, For east x2= -240sin30o = -120m

          north y2 = 240cos30o = 207.8km

Now to determine x- and y- distances from Base Camp to lake B...

xfinal = x1 - x2=364.32

yfinal = y1 + y2=296.73

Now to know the distance from lake B to Base Camp...you use the pathagorean theorem:

distance = ((xfinal)2 +(yfinal)2) = 469.86 km

For the angle measurement...

we know that tan = y/x= 296.73/364.32= 0.81447

= tan-1 (0.81447)

=39.16

so,

D = 469.86km at 39.16 south of west

8.

Given that :

= (-27, 30.4) units

where, Ax = -27 units and Ay = 30.4 units

(a) Magnitude of this vector will be given as :

| A | = Ax2 + Ay2

| A | = (-27 units)2 + (30.4 units)2

| A | = 40.65 units

(b) Direction of this vector will be given as :

Using a trigonometric identity, we have

= tan-1 [(30.4) / (-27)]

= - 48.3

=180+ (-48.3)

=131.6

{Counter clockwise from the +x axis)

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