- #1
midge
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Homework Statement
A baseball is hit at an angle theta. After a time, it lands 7.5m above the point at which it was hit, the land angle is 28 degree below the horizon. The final velocity is 36m/s2. Find the direction and magnitude of the initial velocity.
Know: vf = 36m/s2
theta (final)= 28 degree
H= 7.5m
Unknown: Vo and theta(initial)
Homework Equations
Vxf = Vxi= Vfcos(theta)
Vyf= Vfsin(theta)
Vy^2= [V(initial)sin(theta)]^2 - 2g(yf-yi)
The Attempt at a Solution
I'm breaking down the initial velocity to its component. First I'm finding the x-component of the initial velocity, which is the same as the final Vx since there is not acceleration in the x-direction:
Vx (initial) = Vfcos(theta)
= 36m/s2 * cos(28)
= 31.79 m/s2
Then I'm looking for the y-component of the final velocity, which is:
Vy= Vfsin (theta)
= 36m/s2 *sin(28)
= 16.9m/s2
From there, I find the y-component of the initial velocity:
Vy^2= [Visin(theta)]^2 - 2g(yf-yi)
16m/s2 = Vy(initial)^2 - 2g(7.5)
Vy(initial)^2 = 432.61
Vy(initial)= 20.8 m/s2
To find the initial velocity, I used a2+b2 = c2 for the magnitude and tan(theta)= Vi/Vx for the direction, and the final answer I found is 38 m/s2 at the starting angle of 33.19
***My concern is that I based my solution on the assumption that the landing angle is 28 and so I use that for all my final thetas. Also, I'm not sure using the last equation, to find the initial Vy is valid. Please let me know where I went wrong in this approach. Thank you.