Question

Using pythagoras Theorem, find the two components of the airplane velocity if it takes off with 200 m/sec making 45 degree angle with the horizontal.

Answer 1

given :

initial velocity=200 m/s

initial angle with horizontal=45 degrees

then:

in a right angle traingle with other two angles being 45 degrees, base and height will be of equal length.

if that length is L and the hypotenus is 200 m/s,

using pythogoran theorem:

L^2+L^2=200^2

==>L=sqrt(200^2/2)=141.42

hence horizontal component=vertical component=141.42 m/s

alternative method:

horizontal component=velocity*cos(angle)=200*cos(45)=141.42 m/s

vertical component=velocity*sin(45)=141.42 m/s^2