Ball Thrown up in air, Velocity Question

[cbrowne]

Homework Statement

A ball is thrown vertically upward with an initial speed of 11 m/s. One second
later, a stone is thrown vertically upward with an initial speed of 25 m/s. (a) Find
the time it takes the stone to catch up with the ball. (b) Find the velocities of the
stone and the ball when they are at the same height.

Homework Equations

The Attempt at a Solution

a = 9.8
V_i,ball= 11 m/s V_i,stone= 25m/s

y= y₀+ V₀t+ 1/2 at²

y = 11t+ 1/2 (9.8) t²

y= 11t - 4.9 t² ======= ball

y = 25 (t+1) + (4.9 (t+1))²

y = 25t + 25 - 4.9 ( t² + 2t + 1)

y = 25 t + 25 - 4.9 t²-9.8t - 4.9

y= -4.9t2 + 15.2t + 20.1 ===== stone

11t - 4.9 t2 = -4.9t2 + 15.2t + 20.1



am i on the right track??

 

[LowlyPion]

Sort of.

I think it might be easier to take a snap shot at the start of the second launching.

At that moment the ball is

Y_o = 11*t - ½gt² evaluated at 1 sec

And at 1 sec, the velocity V₁ = 11 - 9.8*t evaluated at 1 sec.

Now you can write your equations all with the same time can't you?

The ball now can be given by:

Y = (11 - ½g) + (11-9.8)*t - ½gt²

The rock:

Y = 0 + 25*t - ½gt²

When they are equal:

25*t - ½gt² = (11-4.9) + 1.2*t - ½gt²

And it looks like the ½gt² disappears.

 

[cbrowne]

so i get t=0.256 ... is this right? so this is the time it takes for the stone to catch up to the ball. how could i figure out B) the velocity?

 

[turin]

You can check your answer for reasonability by drawing a graph. Do you know what kind of curve these trajectories make in the y,t plane? Draw both of them on the same graph (with the proper shift), and you should see a particular point of interest.

 

[cbrowne]

sorry, i have absolutely no idea how to draw that lol

 

[turin]

sorry, i have absolutely no idea how to draw that lol

Hmm. What do you mean by "this"? Of course, the first step would be to decide what is the shape. A mathematical equation y=f(t) for each of the two balls would suffice. Then, you can either use the (antiquated, but useful on tests) skill of sketching this out by hand, or you can use Excel (or some other spreadsheet/plotting program).

 

[LowlyPion]

so i get t=0.256 ... is this right? so this is the time it takes for the stone to catch up to the ball. how could i figure out B) the velocity?

What is the equation for the rock velocity?

V = V_o - a*t

You know t, so ...

 

[cbrowne]

should i add 1 second to my time?

 

[LowlyPion]

should i add 1 second to my time?

You would add 1 sec if you wanted to know how long the ball was in the air.

 

[cbrowne]

o ok.. i think i understand now.. so my answer is then i guess t= 0.256, since it was thrown 1 second after.

 

[LowlyPion]

This was originally why I suggested you consider taking the snapshot at the moment the rock was thrown and solving for t, because that's the answer you are looking for.