Constant acceleration ball throw problem

[Crusaderking1]

Homework Statement

An entertainer juggles balls while doing other activities. In one act, she throws a ball vertically upward, and while it is in the air, she runs to and from a table 5.80 m away at a constant speed of 2.40 m/s, returning just in time to catch the falling ball.

1. With what minimum initial speed must she throw the ball upward to accomplish this feat?

I'm positive the answer is 23.7 m/s.

2. How high above its initial position is the ball just as she reaches the table?

Homework Equations

A constant acceleration equation.

The Attempt at a Solution

After I obtained the speed, I simply plugged it into the equation -9.8(1.2085)²+23.7(1.2085)

and received 14.32 m for problem number 2. Is this right? I don't feel like it is. Thanks!

 

[kuruman]

After I obtained the speed, I simply plugged it into the equation -9.8(1.2085)²+23.7(1.2085)

and received 14.32 m for problem number 2. Is this right? I don't feel like it is. Thanks!

How did you get 1.2085 s?

 

[Crusaderking1]

How did you get 1.2085 s?

Split the time in half.

5.80/2.40 = 2.417, and then halved it.

 

[kuruman]

You halved one time too many. You forgot that she runs a total distance of 5.8+5.8 =11.6 m. So the total running time is 11.6/2.4 not 5.8/2.4.

 

[Crusaderking1]

You halved one time too many. You forgot that she runs a total distance of 5.8+5.8 =11.6 m. So the total running time is 11.6/2.4 not 5.8/2.4.

ooh ok thanks! So I need to plug 2.417 instead of 1.2085 into the equation.

 

[Crusaderking1]

I got 33.6, sound better?

 

[Crusaderking1]

Am I using the wrong equation now? I received wrong answer for using 2.417 in the equation above.

x(t) = vt - (1/2)at^2 + x0 sounds better.

23.7(2.417)-0.5(-9.8)(2.417)^2 + 0?

xo = 0?

 

[kuruman]

Am I using the wrong equation now? I received wrong answer for using 2.417 in the equation above.

x(t) = vt - (1/2)at^2 + x0 sounds better.

23.7(2.417)-0.5(-9.8)(2.417)^2 + 0?

xo = 0?

You have one minus sign too many. In the equation x = x₀+v₀t+(1/2)at² you should replace a with -9.8 m/s².

Yes x0 = 0.

 

[Crusaderking1]

You have one minus sign too many. In the equation x = x₀+v₀t+(1/2)at² you should replace a with -9.8 m/s².

Yes x0 = 0.

Ok thanks a ton! I received 28.7 meters. sound better?

 

[kuruman]

Much better.