M2 Mechanics question(Urgent)

A particle P is projected with the velocity (7i + 7(3^0.5)j)
At time t = 0
the particle is at (xi + yj) at a particle time in its flight
a) show that y = 3^0.5 x - g/98 x^2
b) find y when x = 20

Let me know the working and what you get for b part, theres a c part as well that i cant remember so if anyone finds the question online let me know

Original post by NatoHeadshot

A particle P is projected with the velocity (7i + 7(3^0.5)j)
At time t = 0
the particle is at (xi + yj) at a particle time in its flight
a) show that y = 3^0.5 x - g/98 x^2
b) find y when x = 20

Let me know the working and what you get for b part, theres a c part as well that i cant remember so if anyone finds the question online let me know

Working is easy.

Find the vertical displacement in terms of

t

as you normally would, then using horizontal displacement, you can express t in terms of x. Then just substitute that expression into y to get it in terms of x.

Second part is simple as well. Substitute x=20 into the equation you just found.

Reply 2

NatoHeadshot

OP

15

Original post by RDKGames

Working is easy.

Find the vertical displacement in terms of

t

as you normally would, then using horizontal displacement, you can express t in terms of x. Then just substitute that expression into y to get it in terms of x.

Second part is simple as well. Substitute x=20 into the equation you just found.

yea but i think im still going wrong, can you just maybe work through it quickly or at least give me your finals ans?
apparently that method doesn't work /: question is like 13 marks

(edited 7 years ago)

Reply 3

the bear

20

we are not allowed to give complete answers... just helpful hints ?

consider the horizontal velocity ...it is constant at 7 m/s

consider the vertical velocity... it changes according to v = u + at... u is the initial vertical velocity & a is 9.8 m/s² downwards.

Original post by NatoHeadshot

yea but i think im still going wrong, can you just maybe work through it quickly or at least give me your finals ans?
apparently that method doesn't work /: question is like 13 marks

y=ut+\frac{1}{2}at^2=7x\sqrt{3}-\frac{1}{2}gt^2

x=ut=7t \Rightarrow t=\frac{x}{7}

\Rightarrow y=7(\frac{x}{7})\sqrt{3}-\frac{1}{2}g(\frac{x}{7})^2=x \sqrt{3}-\frac{gx^2}{98}

Reply 5

NatoHeadshot

OP

15

Original post by RDKGames

y=ut+\frac{1}{2}at^2=7x\sqrt{3}-\frac{1}{2}gt^2

x=ut=7t \Rightarrow t=\frac{x}{7}

\Rightarrow y=7(\frac{x}{7})\sqrt{3}-\frac{1}{2}g(\frac{x}{7})^2=x \sqrt{3}-\frac{gx^2}{98}

yea, thanks but the b part is the heavy marked question and my friend said he got it wrong by just substituting into the equation

Original post by NatoHeadshot

yea, thanks but the b part is the heavy marked question and my friend said he got it wrong by just substituting into the equation

If substituting it is a mistake, then either the question or the mark scheme is wrong. The displacement I get is negative but that doesn't really suggest what information is wrong given the little amount of context.

Reply 7

NatoHeadshot

OP

15

Original post by RDKGames

If substituting it is a mistake, then either the question or the mark scheme is wrong. The displacement I get is negative but that doesn't really suggest what information is wrong given the little amount of context.

the question might have been find the direction of motion when x=20

Original post by NatoHeadshot

the question might have been find the direction of motion when x=20

Then work out the time when x=20 and plug it into the velocity equations. Construct a triangle, find the angle and there you have the direction of motion. The angle should be below the horizontal obviously.

M2 Mechanics question(Urgent)

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