Calculate Projectile Velocity: Magnitude & Direction

[scw287]

A diver springs upward from a board that is three meters above the water. At the instant she contacts the water her speed is 9.00 m/s and her body makes an angle of 81.0° with respect to the horizontal surface of the water. Determine her initial velocity, both magnitude and direction.
magnitude m/s
direction °


Here's what I've tried to do: I tried to solve for the initial velocity by using the kinematics equation v^2=vo^2+2*a*x
vo=1.174<<initial velocity

Now I need to find the magnitude and the direction, I think you use tan-1 and pythagorean theorem but I don't really understand the component method very well. Could you please help me get on the right track for this problem. All help will greatly be appreciated.

 

[ice109]

do you know the position function?

 

[scw287]

no I haven't heard of the position function.

 

[ice109]

do you know the kinematic equations?

 

[andrevdh]

How did you get the initial y velocity 1.174 m/s?

 

[scw287]

Yes I know the kinematics equations x=volt+a/2at^2
x=1/2(vo+v)t
v=vo+at
v^2=vo2+2axI got 1.74m/s for the initial velocity by using the fourth equation. I am not positive that I did it right. Not sure what to do next!

 

[skeeter]

in the y-direction ...

v_{fy}^2 = v_{oy}^2 - 2g(Delta y)

v_{oy} = sqrt[v_{fy}^2 + 2g(Delta y)]

v_{oy} = sqrt[(9*sin(81))^2 + 2(9.8)(-3)] = approx 4.5 m/s

velocity in the x-direction is a constant ...

v_x = 9*cos(81) m/s

you now have both x and y components of the initial velocity ... finish up.

 

[scw287]

Thanks for all of your help!

 

[andrevdh]

Yes, I thought that you did use the fourth equation, but I got a different answer. I was hoping that you would show more exactly how you susbtituted to get to it so that we can compare notes.