R1.A.5. An airplane takes off at V = 288 km/h at a 23° above the horizontal. Setup with a labeled diagram.Calculate V is m/s and its horizontal Vx and vertical Vy components.Find the height (h) of the plane 12 min after the takeoff.

Answered: Setup with a labeled diagram. Calculate…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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R1.A.5. An airplane takes off at V = 288 km/h at a 23° above the horizontal.

Setup with a labeled diagram.
Calculate V is m/s and its horizontal Vx and vertical Vy components.
Find the height (h) of the plane 12 min after the takeoff.

Expert Solution

Step 1

Given data:

The aeroplane takes off speed is: $V = 288 km / h$

The angle of takes off is: $θ = 23^{\circ}$

The horizontal component of the aeroplane takes off speed is: $V_{X}$

The vertical component of the aeroplane takes off speed is: $V_{Y}$

The height of the plane 12 min after takeoff is: $h$

(1)The setup with the labelled diagram is drawn below,

(2)The velocity in m/s is calculated as,

$\begin{array}{rcl} V & = & 288 \frac{km}{h} \times (\frac{1000 m}{1 km}) \times (\frac{1 h}{3600 s}) \\ = & 288 \times \frac{5}{18} m / s \\ = & 80 m / s \end{array}$

Thus, the aeroplane takes off speed is 80 m/s.

The horizontal component of velocity in m/s is calculated as,

$\begin{array}{rcl} V_{X} & = & V \cos (θ) \\ = & 80 m / s \times \cos (23^{\circ}) \\ = & 73.64 m / s \end{array}$

Thus, the horizontal component of velocity is 73.64 m/s.

The vertical component of velocity in m/s is calculated as,

$\begin{array}{rcl} V_{Y} & = & V \sin (θ) \\ = & 80 m / s \times \sin (23^{\circ}) \\ = & 31.26 m / s \end{array}$

Thus, the vertical component of velocity is 31.26 m/s.

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