# 2D Kinematics explanation

## Homework Statement

A tennis ball is thrown from ground level with velocity vo directed sin 30 above the horizontal. If it takes the ball 1.0s to reach the top of its trajectory, what is the magnitude of the initial velocity?

## Homework Equations

The initial vertical component of velocity is

(1) Vy,o = Vo sin(30)

As the ball rises gravity slows the ball down until the vertical
velocity is zero. The equation that describes the vertical component
of velocity as a function of time is

(2) Vy = Vy,o - gt

Where g = 9.8m/s^2 is the magnitude of the acceleration due to
gravity and t is time. Now when t = 1s Vy = 0 (this corresponds
to the maximum height) so we have.

(3) 0 = Vy,o -g(1s)

Substituting (1) and g = 9.8m/s^2 into (3) gives

(4) 0 = Vo sin(30) - 9.8 m/s

solving for Vo

(5) Vo = (9.8 m/s)/ sin(30)

= (9.8 m/s)/ 0.5

= 19.6 m/s

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* Vo = 19.6 m/s *
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## The Attempt at a Solution

Why am I using sin 30 - I understand that that is the y direction, but why is it not
0 = Vo - 9.8 (1)
Vo = -9.8, I understand this answer is not reasonable but I want to know the explanation for why I am using sin 30. I hope you understand what I am asking :)

rock.freak667
Homework Helper
The horizontal component of the velocity (the one with cos30 in it) would not change with time. Only the vertical component is changing with time. So you would need to get the final vertical component of velocity at the specific time and then combine it with the constant horizontal component of the velocity to get the velocity.

The horizontal component of the velocity (the one with cos30 in it) would not change with time. Only the vertical component is changing with time. So you would need to get the final vertical component of velocity at the specific time and then combine it with the constant horizontal component of the velocity to get the velocity.

That was exactly what I was after - thank you very, very much :)