Free fall tennis ball problem

[luysion]

Homework Statement

A tennis ball is hit down at
an angle of 30° below the horizontal from a height of 2 m. It
is initially traveling at 5.0 m s−1. What is the velocity of the
ball when it hits the ground if we can neglect air resistance?

Homework Equations

The Attempt at a Solution

ok so I actually attempted it and want to know if my answer is correct as the actual answer is 8.0 i got 8.3, is this just due to rounding errors or is my working wrong;

So I got the final horizontal and vertical components and sumed them to get the resultant/final speed of the ball.

so for the horizontal speed = cos 30deg x 5 = 4.33
for the initial vertical speed = sin 30deg x 5 = 2.5
final vertical speed = 7.5
then sqtr of 4.33^2 + 7.5^2 to give me 8.3
is this correct?

thanks to anyone that checks much appriciated!

 

[Mintea]

Wait, so you multiplied sin 30 * 5 and got 7.5? Are you sure that you put that into your calculator right? The sine of 30 should come out to be 0.5...

You also need to factor the acceleration due to gravity in there somehow. Or did you already put that in somehow with your 7.5 and just not write it?

Also, for it to be a complete velocity and not just a speed, you'd need to include the angle below the horizontal. ;) Hope this helps!

 

[GreatEscapist]

I'm not sure this is done right, but the actual work the way you did it yields 8.66. At least according to my TI-84

 

[luysion]

sorry i typed it wrong haha 7.5 is the final vertical velocity 2.5 is the initial