Question

A vector is described. Express the vector in terms of i and jA quarterback releases a football with a speed of 36 feet per second at an angle of 60° with the horizontal.

Answer 1

Okay, here we have this:

Considering the provided information, we are going to express the vector in terms of i and j, so we obtain the following:

So, let's use the formulas: x=||v||cosθ and y=||v||sinθ, then we have:

x=||36|| cos(60°)

x=36 cos(60°)

x=36 (1/2)

x=18

y=||36|| sin(60°)

y=36 sin(60°)

y=36 (√3/2)

y=18√3

magnitude=√(18^2 + (18√3)^2)

magnitude=√(324 + 324*3)

magnitude=√(324 + 972)

magnitude=√1296=36

Unit vector=(18/36, 18√3/36)

Unit vector=<0.50, 0.87>

Then, finally we obtain the following vector <18, 18√3> and as an unit vector <0.50, 0.87>, V=0.50i+0.87j.