Question

TRIGONOMETRY What is the resultant speed of the plane round to the nearest hundredth

Answer 1

Step-by-step explanation

Let's represent the situation on a graph, we know the plane moves at 150 miles per hour at 100 degrees east of north; but, if we measure from the positive x-axis, this corresponds to a -10 degree angle.

The velocity's x-component is thus as follows:

`150\cdot\cos (-10)=147.72\text{mph}`

The velocity's y-component is thus as follows:

`150\cdot\sin (-10)=-26mph`

Therefore, the velocity vector is as follows:

V = < 147.7 mph, -26 mph >

Now, we need to represent the wind vector, applying the same reasoning than above:

x-component: 50*cos(225°) = -35.4 mi/hr

y-component: 50mi/hr*sin(225°) = -35.4 mi/hr

Therefore the wind vector is as follows:

W = < -35.4 mi/hr, -35.4 mi/hr>

Then, adding both vectors:

resultant V + W = (147.7 -35.4 , -26 -35.4)

resultant V + W = (112.3mph, -61.4mph)

Finally, we need to get the direction of the vector:

θ = tan^-1 (y/x)

Plugging in the numbers into the expression:

`\theta=\tan ^(-1)((-61.4)/(112.3))`

Computing the argument:

`\theta=\tan ^(-1)((-61.4)/(112.3))=-28.7\text{ degre}es`

In conclusion, the direction of the plane is 28.7 degrees south of east