How Do You Calculate Initial Velocity in a Vertical Ball Throw?

[Erenjaeger]

Homework Statement

Concept Simulation 2.3 provides some background for this problem. A ball is thrown vertically upward, which is the positive direction. A little later it returns to its point of release. The ball is in the air for a total time of 8.21 s. What is its initial velocity? Neglect air resistance.

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Homework Equations

x_f=x_o+v_o+1/2at²[/B]

The Attempt at a Solution

known values
x_f = 0 because it comes back to where it was released from
x_o = 0 because initial displacement is going to be 0
a = -9.8m/s²
t = 8.21 s
so couldn't you solve by using the kinematic formula x_f=x_o+v_o+1/2at²
and then solving for v_o
leaving you with -v_o=x_o+1/2at²-x_f
and because both the initial displacement and final displacement are 0
-v_o = 1/2 at² ?
so -v_o=-9.8⋅8.21²
which gives me -330.62 which would be just 330.62m/s but it is incorrect. pls helpp[/B]

 

[TSny]

x_f=x_o+v_o+1/2at²

Can you spot the mistake in this equation?

 

[Erenjaeger]

a

Can you spot the mistake in this equation?

ahhhh i haven't put in v_o t
because the equation is really x_f=x_o+v_ot+1/2at² right?

 

[TSny]

ahhhh i haven't put in v_o t
because the equation is really x_f=x_o+v_ot+1/2at² right?

Yes, good.

 

[Erenjaeger]

Yes, good.

so by just dividing my answer by t (8.21) ill get the v_o right?

 

[TSny]

so by just dividing my answer by t (8.21) ill get the vo right?

Yes. But be careful with the signs. In your first post you wrote

so -v_o=-9.8⋅8.21²which gives me -330.62

But you have a negative sign on both sides, so this will give a positive value for v₀.

 

[Erenjaeger]

Yes. But be careful with the signs. In your first post you wrote

But you have a negative sign on both sides, so this will give a positive value for v₀.

yeah okay, thank you!