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

Horizontal component of velocity =1.7364m/s

Vertical component of velocity =9.848m/s

Step-by-step 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*`cos(80°)

`1.7364m/s`

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

`v_(y)=10*`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