Question

A plane moves at a speed of 100 mi/h and takes flight on a 25 degree angle. What is the VERTICAL speed in mi/h? Round to the nearest whole number and DO NOT include units (Ex: 11).​

Answer 1

The vertical speed in mi/h is 42.

Step-by-step explanation:

Rectangular Components of a Vector

A 2D vector can be expressed in several forms. The rectangular form gives its two components, one for each axis (x,y). The polar form gives the components as (r,θ) being r the magnitude and θ the angle.

The relationships between the coordinates of both systems are shown in the image below.

When the magnitude and angle of the vector are given, the rectangular components are calculated as follows:

`v_x=v\cos\theta`

`v_y=v\sin\theta`

Where v is the magnitude of the vector and θ is the angle with respect to the x positive direction.

We are given the magnitude of the velocity (the speed) at which a plane is moving as v=100 mi/h at an angle of θ=25°, the vertical component of the velocity is:

`v_y=100\sin 25^\circ`

Calculating:

`v_y=42.26\approx 42`

The vertical speed in mi/h is 42.