projectile motion (1 Viewer)

[sasquatch]

Could somebody please check this, i think the answer in the book is wrong.

2. A cricketer can throw a ball 40 m vertically upwards. What is his maximum throwing range on a flat cricket field.

Let V represent the initial velocity.
Maximum range occurs when @ = 45 degrees

so,
u_y = Vsin45 = V/root2
u_x = Vsin45 = V/root2

At heighest point, v = 0,

0 = u_y² + 2(-9.8)(40) [using v² = u² + 2as]

u_y² = 784
therefore u_y = 28 m/s

but u_y = V/root2 = 28
therefore u_x = 28 m/s

Travel time:

-28 = 28 -9.8t [using v = u + at]
-56 = -9.8t
t = 56/9.8

Hence,

range_max = 28 * 56/9.8
= 160 m

The answer at the back is 80m but i cant see that i made any mistakes

 

[Riviet]

I believe you are correct.

 

[hyparzero]

I believe you are correct.

even so, if thats the working out in an exam, you'll be probably be awarded no marks.

 

[sasquatch]

yes yes i know you need to derive everything..but im doing a set of exercises. why the hell would i derive the same set of equations 14 times...

When you derive the projectile equations can you first derive v = u + at, s = ut + (1/2)at² and v² = u² + 2as and then use the fact that the inital velocity in the y direction is Vsin@, and in the x direction Vcos@ to solve the questions. Or would you need to do it in this way:

d²y/dt² = -g
dy/dt = -gt + c

when t = 0, dy/dt = Vsin@, therefore c = Vsin@

dy/dt = -gt + Vsin@
y = -(gt/2)² + Vtsin@ + d

when t = 0, y = 0, therefore d = 0,

and etc. because i think the first way is easier.

 

[hyparzero]

yes yes i know you need to derive everything..but im doing a set of exercises. why the hell would i derive the same set of equations 14 times...

for fun

 

[Riviet]

i think the first way is easier.

Well of course they're much more convenient to use, it would be a simple excercise of subbing values in. In an exam, you need to do it the long way, ie by integrating the vertical and horizontal components of the accleration, etc.

 

[sasquatch]

No but i meant find the equations:

v = u + at
v² = u² + 2as
s = ut + (1/2)at²

using the fact that d²y/dt² = a, and integrating to form v = u + at, and s = ut ...... and using those two results to show v squared thingo, and THEN subsitute in the velocities to solve the questions?

Its kinda the same but it forms everything more generally and also allows a result similar to v² = u² + 2as to be more easily formed.

So if you didnt get what i said in the previous post, is it ok to do what i said above to solve equations involving projectile motion?

 

[Riviet]

I'm not sure if you're allowed to derive those 3 formulae, but you are definitely not allowed to just use them without derivation at all. I would suggest to stay away from them, even if you derive them.

 

[sasquatch]

aww my book has all that crap in it..and i swear its easier and it makes everything the same as physics.. but ah well i guess ill ask my teacher or something after school resumes.

thanks though!!!

 

[STx]

aww my book has all that crap in it..and i swear its easier and it makes everything the same as physics.. but ah well i guess ill ask my teacher or something after school resumes.

thanks though!!!

The method is not meant to be the same as in the physics course we do.

 

[who_loves_maths]

The method is not meant to be the same as in the physics course we do.

But what's with that though?

Clearly it's just mathematicians practicing hubris again...

Can't Physics and Mathematics just get along on the HS level ?

 

[STx]

^lol yeah, its the just because of the 'watered down' physics course in terms of the mathematics involved, otherwise it would be the same as maths.

 

[Irskin]

Hey sasquatch. The answer is 80m.

You have calculated the time of flight of both the up and down motion of the ball when the cricketer threw it straight up. You need to half your time for just the ball getting to the top of its motion and then substitute it into X= Uxt to get 80m (half your time to get half your answer and the correct one)

However, when doing projectile motion in both maths and physics it is best to keep your formulae separate. When doing maths, always derive the equations using integration. If you had done this you would have come up with:

Maximum range (x) = V^2/g

= 28^2/9.8

= 80m

 

[sasquatch]

Yeah i found "Whole" time of flight. Why would you just find the time of flight up to the maximum point? Cuz the question doesnt say calculate the range up to the highest point it just says the range (which is the horizontal distance it travels)? Maybe i didnt understand what you said though..but yeah...

And also regarding the crappiness of physics..hehe. Yeah i hate the australian course for physics its so retarded. If they taught the math side to things it would make much more sense and be easier to understand. The explination of gravitational potential energy is so stupid. If you see the maths behind it it makes it seem much more clearer.

 

[who_loves_maths]

^ But I think you have to be carefully though, when criticising "Australian" HS physics, since different states and territories have different assessable outcomes and curricula.
This applies to maths as well - e.g. in NSW there is no evidence of statistics, or elements of linear algebra (e.g. matrices), in the syllabus of senior high school, whereas other states such as S.A. and W.A. teach these important areas of pure and applied mathematics.

Also, what is at issue here with gravitational potential energy and the way it is taught in HS???
I thought the syllabus simply says that the derivation of the expression for GPE is "beyond the scope of syllabus"? How is that explanation "stupid" in your words?

And the definition given to GPE, as I remember it from last year, is quite correct - i.e. that GPE is defined to the the amount of work against the gravitational field needed to bring an object outside it to some position inside it a finite distance away from the source of the field.
There is nothing wrong with this definition, it is an international standard.

 

[sasquatch]

Yeah i didnt mean to generalise.. i meant NSW or well whatever course it is IM doing. About the GPE definition, its fine to say that it is the measurement of the work required to bring an object from an infinite distance to a point within the field. But there is not explination in 'why' it is like this. Also just cuz the syllabus doesnt have an explination of 'why' something is the way it is (which occurs for many of the dot points) doesnt mean that it shouldnt matter. Its sufficent i guess to know 'what' to do well in the HSC examination, but it really doesnt help when a student say chooses physics electives (or does a complete physics course) within uni as it would involve repeated or furthered learning of the same topics which could be much easily avoided by learning it properly in high school.

It would be silly to say though "just because a person does physics in high school, doesnt mean they will do something related to physics in university" as that is as pointless as saying "just because someone does an engineering course in uni, doesnt mean that they will become an engineer". Well yeah i think im straying away from my point. Hehe all i wanted to say is that im unhappy with the way physics is taught for the hsc course.

 

[who_loves_maths]

1) About the GPE definition, its fine to say that it is the measurement of the work required to bring an object from an infinite distance to a point within the field. But there is not explination in 'why' it is like this.

...

2) Hehe all i wanted to say is that im unhappy with the way physics is taught for the hsc course.

1) There is a reason I italicised the word "defined" in my last post sasquatch as I knew something of the nature of your statement 1 would come up:
It is a definition - a logically 'sufficient' formulation of the concept of GPE so as to be reconcilable with the quantatitive theory behind it. Definitions, as they are in mathematics as well, are objects which are simply taken to be - without need for reason nor 'proof'.

The important thing to realise is the fact that when you integrate the expression for the gravitational force and obtain an expression for GPE, the fact that substituting a limit of infinity into the expression yields 0 GPE at infinite distance is NOT what underpins the concept of GPE (which I assume is what you were initially thinking about when you said all things come to light when one looks at the derivation of the GPE expression?).

In fact, one may take the GPE to be of any value at infinite distance and fit a theoretical model to work with such a definition.

It is the definition itself that underpins the model we use, not the other way around.

In the case of this particular definition - to take GPE to be 0 at infinity - it is simply an act of convenience that we do this, since 0 is an aesthetic number to assign to anything to do with infinities.
So there is no reason as to "why" we do it that could not be achieved by simple convenience or elegance of idea that can be by "looking at the derivation" of the expression.


2) As for your statement 2: join the club!

 

[sasquatch]

Well i dunno i got it round the wrong way i guess.. but it still makes it easier to understand by knowing the maths behind things.

 

[who_loves_maths]

True.