Initial Speed of Ball Thrown Horizontally from 15.75m Height

[Eleet]

A ball is thrown horizontally from a height of 15.75 m and hits the ground with a speed that is 5.0 times its initial speed. What was the initial speed?


I thought you might have to find time and I got t=1.79s, but after that I cannot seem find my way to the answer

Thanks to whom ever can help me out,

Eleet
Shaun

 

[Doc Al]

The fact that the ball is thrown horizontally tells you that the vertical (y) component of the initial velocity is zero. So the initial velocity is purely x-component. Find the vertical component of the final velocity considering that the ball falls the given distance. (Hint: use a kinematic equation relating speed and distance for accelerated motion.)

 

[Eleet]

??

I do not know if this right but I found:
Vf=17.58m/s
by using Vf^2=2ad.

Than how do I use this to find initial velocity horizontally. Or is that it?

 

[ExtravagantDreams]

the initial velocity will be what ever it is, this same velocity is also part of the final.

so $\Vec {V_f}: [V_x,V_y] = 5\Vec {V_i}: [V_x,0]$

 

[Tide]

the initial velocity will be what ever it is, this same velocity is also part of the final.

so $\Vec {V_f}: [V_x,V_y] = 5\Vec {V_i}: [0,V_x]$

Be careful! That's 5 times the speed - not velocity! :-)

 

[ExtravagantDreams]

right, but the initial speed is a velocity with only one component, namely the x
But I did put them in the wrong order

 

[Tide]

More to the point: $$v_x^2+v_y^2 = 25 v_x^2$$

 

[Doc Al]

Vf=17.58m/s
by using Vf^2=2ad.

What you found is the y-component of the final velocity. Good! The final velocity has two components: $v_x$ (which is just the initial speed) and $v_y$ (which you just found).

Than how do I use this to find initial velocity horizontally. Or is that it?

Now apply what was given in the problem statement: that the final speed is 5 times the initial speed. Tide gives you the formula:

More to the point: $$v_x^2+v_y^2 = 25 v_x^2$$

Note that the initial speed is $v_x$, which is what you're trying to find.

Do you understand how Tide got his formula?

 

[Eleet]

undefinedundefinedI got it.

we know height so we need to use this formula:

(5Vo)^2=Vo^2+ g2h
>>> Subtract out the Vo^2
>>>>24Vo^2=2gh
>>>>>Vo^2=2gh /2

then, Vo=3.6m/s :laughing: