Projectile Motion of Pebbles: Solving for Initial Velocity and Impact Velocity

[tica86]

Romeo is tossing pebbles at Juliet's window and wants the pebbles to hit the window gently, with only a horizontal component to their velocity, as they hit the window.

He is standing at the edge of a rose garden 4.5m below her window and 5.0m from the base of the wall.

--------I know that final vertical velocity=0m/s
---------acceleration = -9.8
---------vertical displacement= 4.5m

My attempt:


1) What is the y component of the initial velocity of the pebble as it leaves romeo's hand?

Do I use, vi = sqrt(2ay)
where a=-9.8 but how do I find y?


2)How long does the pebble take from the time it leaves Romeo's hand to hit the window?


Do I use t = vi/g, but first I need to find #1 to solve for time

For questions 3-5 I really have no idea how to solve

3)What is the velocity with which the pebble hits the window?

4)Find the magnitude of the velocity with which Romeo tosses the pebble up?

5)Find the angle at which Romeo launches the pebbles?


I have been trying to solve it for the last couple of hours and I don't get it, I would appreciate any help, thanks!

 

[zgozvrm]

Given an initial velocity [itex]V_{iy}[/tex] and assuming that the projectile, if unobstructed, will land some horizontal distance away at the same vertical height that it was launched, how would you determine the time of flight?

 

[tica86]

Given an initial velocity [itex]V_{iy}[/tex] and assuming that the projectile, if unobstructed, will land some horizontal distance away at the same vertical height that it was launched, how would you determine the time of flight?

If I don't have initial velocity I can't solve for time

 

[zgozvrm]

If I don't have initial velocity I can't solve for time

But if you did, how would you do it? What is the formula?

 

[tica86]

But if you did, how would you do it? What is the formula?

Could I use t=2d/-9.8? so 2(4.5)/-9.8

 

[tica86]

Could I use t=2d/-9.8? so 2(4.5)/-9.8

Wait, that's not right...

 

[tica86]

Could I use t=2d/-9.8? so 2(4.5)/-9.8

It's t = (vfy - voy) /a correct?

 

[zgozvrm]

Not quite. Consider the equation

$$D_y = V_{oy}t - 4.9t^2$$

If a projectile was fired from ground level and returned to ground level, what would the vertical displacement be? Then, using the equation, how much time would that take?

 

[tica86]

Not quite. Consider the equation

$$D_y = V_{oy}t - 4.9t^2$$

If a projectile was fired from ground level and returned to ground level, what would the vertical displacement be? Then, using the equation, how much time would that take?

1) what is the y component:
Is it Vv0=0+2(-9.8)(4.5) square root =9.39?
Is acceleration negative?

2) Time:
4.5=.5(9.8)t^2
4.5/4.9
t^2=sq. root=.958seconds??

3) What is the velocity in which the pebbles hit the window?

v=d/t
v=5.0m/.958=5.21m/s??

4) What are the resultant of the 2 components of Vo??

 

[zgozvrm]

Looks good so far, keep going...

 

[tica86]

Looks good so far, keep going...

So for #1 is acceleration negative??

4) Is it,
9.39^2+5.21^2=115.31, square root= 10.7m/s

is that the magnitude?

 

[zgozvrm]

So for #1 is acceleration negative??

4) Is it,
9.39^2+5.21^2=115.31, square root= 10.7m/s

is that the magnitude?

Yes, and yes

 

[zgozvrm]

So for #1 is acceleration negative??

The stone is being thrown upward, which is thought to be in a positive direction on the y-axis. However, the effect of gravity is slowing it down, therefore it is decelerating, or accelerating in a negative direction. (If the acceleration were positive, the stone's velocity would increase as it continued its upward flight).

 

[tica86]

The stone is being thrown upward, which is thought to be in a positive direction on the y-axis. However, the effect of gravity is slowing it down, therefore it is decelerating, or accelerating in a negative direction. (If the acceleration were positive, the stone's velocity would increase as it continued its upward flight).

Ok, thanks for your help! :)