Calculating Projectile Angle and Velocity with Vertical Launch: Explained

[rea]

Ok, after some work, it seem that I am not able to do this exercises, over even get something that describe them...

If a projectile explode at and height of h the movement was vertical (the highest point in the vertical direction is h). The pieces fall in all directions, but all of them have the same speed v. The resistance of the iar is despreciable. Calculate the most short angle (¿acute?) that the velocity will form with the ground.

I don't know even how to handle it... I can see what is asked in some way, but don't know what to plug.The next one, I'm more near, but unable to continue.

From a height y=h a particle is launched vertically, what is the time and velocity for the particle to do contact with y = 0.

here is what I have so far:
Deducing...
a_y = -g
v_y = -gt+V_0
y = -\frac{1}{2}gt^2+v_0t

If V_y eq 0 then the particle is at y_{max} and t_{max} is the time for get there...

0 = -gt_{max} + v_0
t = \frac{v_0}{g}

then
y_{max} = -\frac{1}{2}g\left(\frac{v_0}{g}\right)^2+\frac{v_0v_0}{g}
= \frac{v_0^2}{2g}

[/tex]

Now follow a new problem, where d = h + y_{max}
With start conditions...

<br /> a = g
v_0=0
t_0=0
p_0 = 0

And in the other end of the line:
a=g
v_f = ?
t_f = ?
p_f = d = h + y_{max}I know that this is easy, but now what?

 

[hippolyta2078795]

Yeah. Just set y=0 and solve from there. Use y=y0 + V0T + (1/2)aT^2. Solve for T.

I think you're forgetting some information in the other problem.

 

[rea]

I only don't put the answer that need be proved (I write it in short).

Perhaps my translatio to english in the question is wrong...

Calculate the most short angle (¿acute?) that the velocity will form with the ground.

Here is again:

calculate the shortes (the littlest) angle that the final velocity of a fragment will do with the horizontal. Solution tan^{-1}\left[\left(2gh\right)^{\frac{1}{2}} / v \right].

Perhaps that.

 

[lightgrav]

If a piece leaves the explosion traveling with its velocity straight DOWN,
what is the angle that its final velocity makes with the ground?

If a different piece leaves the explosion with initial velocity straight UP,
what is the angle that its final velocity makes with the ground?

If some piece leaves the explosion with its initial velocity HORIZONTAL,
what is the angle that its final velocity makes with the ground?

Which final velocity angle is smallest?
Can you find the final velocity angle as a function of initial velocity angle?
If so, you can show that horizontal initial velocity should give the smallest final angle, if it is not obvious already (you do want the largest horizontal component, right? and the smallest vertical component...) set \frac{d\theta_{final}}{d\theta_{init}} = 0