Question

A soccer player kicks the ball with a velocity of 10 m/s at an angle of 80 degreees to the horizontal. Find the horizontal and vertical components of the velocity of his kick.

Answer 1

Answer:

Horizontal component of velocity =1.7364m/s

Vertical component of velocity =9.848m/s

Explanation:

As the ball is a 2D projectile,it has two components.

Concept of components of a vector:

1)All the possible independent components of a vector sum up to give the vector.

2)If the magnitude of a vector is v,then its component in the direction at an angle of Θ from the vector is equal to - vcos(Θ).

Now as the ball is having 2D motion,it has two independent components one along the horizontal,one along the vertical.

Given angle of velocity with horizontal $\alpha$=$80$°

Therefore angle of velocity with vertical $\beta = 90$°$-80$°

$\beta =10$°

Therefore,

Component of Velocity along horizontal = $vcos(\alpha )$

$v_{x}=10\times$cos(80°)

$1.7364m/s$

Component of velocity along vertical = $vsin(\beta )$

$v_{y}=10\times$cos(10°)

$v_{y}= 9.848m/s$

Therefore

Horizontal component of velocity of ball$v_{x}$ =1.7364m/s

Vertical component of velocity of ball$v_{y}$ =9.848m/s