Question

1. Find the component form of the vector that represents the velocity of an airplane descending at a speed of 100 mph at an angle of 45° below the horizontal. (Leave answers in exact form)

Answer 1

Answer:

<70.71, -70.71>

Step-by-step explanation:

The vector has a module of 100 and a angle of -45° (negative because it is below the horizontal). So, to find its components, we need to use the sine and cosine relation of its angle:

horizontal component = module * cos(angle)

horizontal component = 100 * cos(-45)

horizontal component = 70.71

vertical component = module * sin(angle)

vertical component = 100 * sin(-45)

vertical component = -70.71

So the vector in the component form is <70.71, -70.71>

The negative sign of the vertical component means its direction is downwards.

Answer 2

The component form should be <70.71, -70.71>

• The calculation is as follows:

horizontal component = module ( cos(angle))

= 100 (cos(-45))

= 70.71

And,

vertical component = module (sin(angle))

= 100 (sin(-45))

= -70.71

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