SUVAT motion question - Ball thrown vertically

[TheGreenMarin]

Homework Statement

A cricket ball is thrown vertically upwards and returns in 4.2s. Find (a)The initial velocity of the ball

(b)The maximum height reached

Homework Equations

v=u+at
v^2=u^2+2as
s=(u+v)/2 multiplied by t
s=ut+1/2at^2

The Attempt at a Solution

s=?
u=?
v=?
a=9.81ms^-2 (negative traveling upwards)
t=4.2s

I could not start the question because to use SUVAT equations at least 3 of the 5 letters must have values to be put into a equation.

 

[Uniquebum]

Start with

v = v_0 + at
Where v = end velocity, v_0 initial velocity, a = g = gravity and t = time

If you consider v to be the velocity at the top of the throw then v = 0.
Thus 0 = v_0 + at
v_0 = -at, You know the acceleration and t = half the total time. So there you get the initial velocity and rest becomes simplier.

 

[Doc Al]

There are two equations you can use.
First fill in these:
s = ?
v = ?
(You have enough information to fill in these values.)

 

[grzz]

THINK!
What is the velocity at the max height?

 

[TheGreenMarin]

There are two equations you can use.
First fill in these:
s = ?
v = ?
(You have enough information to fill in these values.)

s= I'm really not sure how to found out the displacement
v=0 [ as it has stopped at its maximum point in the air?]

 

[TheGreenMarin]

THINK!
What is the velocity at the max height?

0 velocity?

 

[TheGreenMarin]

Start with

v = v_0 + at
Where v = end velocity, v_0 initial velocity, a = g = gravity and t = time

If you consider v to be the velocity at the top of the throw then v = 0.
Thus 0 = v_0 + at
v_0 = -at, You know the acceleration and t = half the total time. So there you get the initial velocity and rest becomes simplier.

0 = v_0 + 9.81x4.2 ? I am not sure I have done this correctly

so v_0 = -41.202 <---- I've definitely gone wrong here, the initial speed surely cannot be negative

 

[Doc Al]

0 = v_0 + 9.81x4.2 ? I am not sure I have done this correctly

so v_0 = -41.202

It looks like you are trying to use this equation: s=ut+1/2at^2

But you left out a few things. Try again. (But yes, s = 0 for the round trip.)

 

[TheGreenMarin]

It looks like you are trying to use this equation: s=ut+1/2at^2

But you left out a few things. Try again. (But yes, s = 0 for the round trip.)

Ah, thankyou s now makes sense

 

[TheGreenMarin]

0=u x 4.2 + 0.5 x 9.81 x 4.2^2

gives me 0 = u x 90.7242

so u = 0

I'm really struggling with this question, what error have I made this time?

 

[Doc Al]

0=u x 4.2 + 0.5 x 9.81 x 4.2^2

OK, except that you have the wrong sign for the acceleration. Fix that first.

gives me 0 = u x 90.7242

No it doesn't. Try again.

 

[TheGreenMarin]

OK, except that you have the wrong sign for the acceleration. Fix that first.


No it doesn't. Try again.

-9.81 as its against gravity, rookie error

I now got -82.3242 as my answer but I'm not sure how this can be right as it is negative

 

[Doc Al]

-9.81 as its against gravity, rookie error

Good.

I now got -82.3242 as my answer

Show how you got that, step by step.

 

[TheGreenMarin]

0=u x 4.2 + 0.5 x -9.81 x 4.2^2

so 0 = u x -82.3242

 

[Doc Al]

0=u x 4.2 + 0.5 x -9.81 x 4.2^2

OK.

so 0 = u x -82.3242

Not OK.

Try this:
0=u x 4.2 + 0.5 x -9.81 x 4.2^2
which I'll rewrite as:
0 = 4.2u -(0.5)(9.81)(4.2^2)
4.2u = (0.5)(9.81)(4.2^2)

And so on...

 

[TheGreenMarin]

OK.

Not OK.

Try this:
0=u x 4.2 + 0.5 x -9.81 x 4.2^2
which I'll rewrite as:
0 = 4.2u -(0.5)(9.81)(4.2^2)
4.2u = (0.5)(9.81)(4.2^2)

And so on...

Just confused on where the - sign has come from in the line: 0 = 4.2u -(0.5)(9.81)(4.2^2)

 

[Doc Al]

Just confused on where the - sign has come from in the line: 0 = 4.2u -(0.5)(9.81)(4.2^2)

Starting with:
0 = 4.2u +(0.5)(-9.81)(4.2^2)

You can move that minus sign from in front of the 9.81 and place it here:
0 = 4.2u -(0.5)(9.81)(4.2^2)

(1)(2)(-3) is the same as -(1)(2)(3).

 

[TheGreenMarin]

4.2u = 86.5242

/4.2 = 20.601 ms^-1 Final answer for (a) I think?

 

[TheGreenMarin]

Starting with:
0 = 4.2u +(0.5)(-9.81)(4.2^2)

You can move that minus sign from in front of the 9.81 and place it here:
0 = 4.2u -(0.5)(9.81)(4.2^2)

(1)(2)(-3) is the same as -(1)(2)(3).

Right OK, I see how you have done that. Is my answer of 20.601 correct?

 

[Doc Al]

Right OK, I see how you have done that. Is my answer of 20.601 correct?

Yes. (I'd round it off to no more than 3 sig figures.)

 

[TheGreenMarin]

Yes. (I'd round it off to no more than 3 sig figures.)

Thank you very much for your help I really appreciate it. I am so glad I found this website, you have helped me greatly. I will definitely stick around here and maybe one day even help people out with their problems (Once I understand the basics).

This site is so helpful that I will tell my friends to come here if in need of any physics help.

Once again thank you Sir, you have really helped me out in understanding of SUVAT equations and of basic re-arranging.

Thank you

 

[Doc Al]

You are most welcome!