Throwing a Ball from a Roof: Calculating Velocity & Angle

[bricker9236]

Homework Statement

A ball is thrown OFF a roof at a height 35.0m above ground. The ball hits the ground 29m from the base of the building. the max height of the balls trajectory is 12 m above the height from which the thrower released it.

a) find the initial vertical component of the velocity.
b) find the total time that the ball is in flight (from the time it is thrown until it lands on the ground)
c) find the horizontal compoent of the initial velocity required for the ball to land 29 m away from the building.
d) at what angle is the ball thrown from the roof? (measure angle above horizontal =0 degrees)

Homework Equations

Not sure, I was just randomly trying to figure it out and this problem frustrated me.

The Attempt at a Solution

a) 10.9 .. that is the answer i got, if anyone could confirm or help me out.
b) 2.22 seconds
c) 14.23 m/s not sure, again
d) 40 degrees again, not very sure .. i used tan inverse of 12/29 wasnt sure if it shiould be tan inverse of (35+12)/29 not sure

 

[rock.freak667]

Homework Equations

Not sure, I was just randomly trying to figure it out and this problem frustrated me.

So let's use these

$$y=y_0 +ut -\frac{1}{2}gt^2$$

$$v^2=u^2-2g(y-y_0)$$

$$v=u+at$$

u=initial velocity
v=final velocity
y₀=initial height.

The Attempt at a Solution

a) 10.9 .. that is the answer i got, if anyone could confirm or help me out.
b) 2.22 seconds
c) 14.23 m/s not sure, again
d) 40 degrees again, not very sure .. i used tan inverse of 12/29 wasnt sure if it shiould be tan inverse of (35+12)/29 not sure

Can't really check your answers if you yourself don't know how you got them.


Now we start, let's call the vertical component of velocity v_y and the horizontal v_x

We are given the maximum height as 12m from the height thrown. What do you know about the final vertical velocity at the maximum height?

 

[bricker9236]

the final vertical velocity at max height would be 0 bc at any max height the velocity is always 0

 

[rock.freak667]

the final vertical velocity at max height would be 0 bc at any max height the velocity is always 0

Right, so using v_y=0, in our possible equations containing v, we can get

$$0=u^2-2g(y-y_0)$$


or

$$0=u+at$$


Which would you like to use or which do you think is better to use?