I don't have a clue how to find the coordinates

[lioric]

Homework Statement

http://i277.photobucket.com/albums/kk63/lioricsilver/Untitled_zps7cf41f04.png

Homework Equations

y2=(16)x is the equation on the question

The Attempt at a Solution

I have got any clue. I do know how to solve motion in 2d. But since time is not given or the height is not given I don't know how to apply any of what i know to this question.

But my hypothesis is that since the hyperbola has an equation given i should use it to find minnimum of the curve. But that's all i got. Sorry but i found all attempts a dead end befor i begin because there is so less values to work with

 

[SteamKing]

What condition must hold when the melon hits the bank?

If you were to find the path of the melon when it is launched horizontally with the given initial speed, could you calculate the x and y values of the trajectory, ignoring the shape of the bank?

 

[tms]

But since time is not given or the height is not given I don't know how to apply any of what i know to this question.

The problem is not particularly well-worded. The vertex of the parabola must be the point where the melon takes off, as shown in the picture, not the edge of the road, as stated in the problem description. So the origin of the system is also as shown in the picture, and therefore the initial height is zero. (Of course, in general the actual location of the origin is arbitrary, but here it makes sense to locate it at the vertex of the parabola.)

You have, or can get, an equation for the trajectory of the melon, and an equation for the stream bed. What must be true, as SteamKing asked, when the melon meets the ground?

 

[lioric]

Ok after analyzing the data i got here is what i know and don't knowObject horizontal stuff

constant velocity V=10m/s
Acceleration a=0
Time t=?
Distance s=?

Vertical Stuff

Initial Velocity U=0
Final velocity V=?
Acceleration = 9.81m/s2(10m/s2)
Time t=?
Distance s=?

But i do know that the time taken for both is the same

Know where do i go from here?

 

[tms]

Start by writing down the relevant equations. Those would be the kinematics equations that relate position, velocity, acceleration, and time.

 

[lioric]

I did try v=u+at for the vertical velocity

so v=0+10 x t
v=10t

also for vertical i tried s=ut+1/2at2
so s=0t+1/210t2
s=0+5t2
s=5t2

also i tried v2=u2+2as
so v2=0+2 x 10 x s
v2=20s

what do i do now?

 

[lioric]

I also mixed up the first 2 equations

v=10t and s=5t2 by substituting in the place of t and got
v=10 x √ s / √ 5

square all to get rid of root and got

v2=100 x s/5

substitute this with 3rd equation v2=20s

and got 400s2= 100s/5

so make subject s

and by now i feel faint

 

[lioric]

some one please give me hand please. I need some sort of guidance for this

 

[SteamKing]

Reread post #2

 

[lioric]

Ok here is some more info.

that equation that is given holds the final key

y2=16x

so i guess i need to put distance in x and y even in terms of s and solve

Plz tell me if this could work

And i couldn't understand what steamking asked in post 2

Well the question says the melon splatters on the bank

 

[SteamKing]

What can we say about the x and y coordinates of the melon and the x and y coordinates of the bank when the melon hits the bank?

 

[SammyS]

The problem is not particularly well-worded. The vertex of the parabola must be the point where the melon takes off, as shown in the picture, not the edge of the road, as stated in the problem description. So the origin of the system is also as shown in the picture, and therefore the initial height is zero. (Of course, in general the actual location of the origin is arbitrary, but here it makes sense to locate it at the vertex of the parabola.)
...

It looks to me as if the problem is worded just fine. It's the art work that doesn't fit the problem too well.

I did try v=u+at for the vertical velocity

so v=0+10 x t
v=10t

No. The horizontal component of v is a constant: v_x = 10 m/s .

The x coordinate of the melon, as a function of time is

x = v_x∙t

x = 10∙t .​

also for vertical i tried s=ut+1/2at2
so s=0t+1/210t2
s=0+5t2
s=5t2

Note: use the X² icon for super scripts.

You are almost correct regarding the vertical position of the melon. (Of course the melon's vertical coordinate goes down from zero, not up.)

So the y component of the melon is

y = -5∙t²​

.

Solve x = 10∙t for t and plug that into the equation for y, to find the path taken by the melon.

You now have two simultaneous equations in x and y to solve .

 

[lioric]

Thank you very.
I have got it by now the only thing that was bothering me was the equation of the parabola.
But i got it now

 

[lioric]

Could i post all my working and final answer so that you could tell me if it is right or wrong?

 

[SammyS]

Could i post all my working and final answer so that you could tell me if it is right or wrong?

Yes, that is perfectly fine.

 

[lioric]

ok here is the answer. please check it out for me

 

[lioric]

Distance in x axis
s=ut+1/2at²

s=? U=10 t=? a=0

∴ s=10t

Distance in y axis
s=ut+1/2at²

s=? U=0 t=? a=9.8

s=9.8/2 t²

t in x-axis and t in y-axis is same

substitute distance in x and y of y²= 16x

y²= 16x

(9.8/2 t²)² = 16 x 10t

24.01t⁴=160t

make subject t

24.01t⁴/t= 160

24.01t³=160

t³=160/24.01

t³= 6.664

t=3√6.664

t=1.88s

----------------------------------

substitute t= 1.88s in equations in x and y axis

s=10t

10x 1.88

=18.81

s=9.8/2 t²

9.8/2 (1.88)²


x= 18.81
y=17.35

is this correct?

I gave everything in very detail so you can tell me where i went wrong.

 

[SammyS]

Distance in x axis
s=ut+1/2at²

s=? U=10 t=? a=0

∴ s=10t

That's for the x coordinate of the melon.

Therefore, x = 10t for the melon.

Distance in y axis
s=ut+1/2at²

s=? U=0 t=? a=9.8

s=9.8/2 t²

That's for the y coordinate of the melon, except that it should be -9.8/2 t².

Therefore, y = -9.8/2 t² for the melon.

...

Solve x = 10t for t.

Substitute that into y = -9.8/2 t².

That will give y in terms of t, for the melon's trajectory.

Take this result together with the equation for the river bank.

This gives two equations in two unknowns. Solve for x any y. (There are two solutions.)