Question

Find the component form of the vector that represents the velocity of an airplane at the instant its wheels leave the ground, if the plane is going 75 miles per hour and the body of the plane makes an9° angle with the horizontal.

Answer 1

The component form of the vector that represents the velocity of the airplane is
`(74.1 i , \ 11.73j)\ mph`

Explanation:

Given;

velocity of the airplane, v = 75 mph

direction of the plane, θ = 9°

The vertical component of the velocity is given by;

`V_y = vsin\theta\\\\V_y = (75)(sin \ 9^0)\\\\V_y = 11.73 \ mph`

The horizontal component of the velocity is given by;

`V_x = vcos \theta\\\\V_x = (75)(cos9^0)\\\\V_x = 74.1 \ mph`

Therefore, the component form of the vector that represents the velocity of the airplane is given as;

`(V_x , \ V_y) = (74.1 , \ 11.73)\ mph`