Competition - post a photo you've taken of nature >>

Awkward M2 projectiles question

This is a question from the Edexcel June 2012 paper. I can't figure out how to do part (c) and the mark scheme/worked solutions haven't helped. The horizontal velocity, speed of projection and time of flight are 10 m/s, 2√74 m/s and 5 s, from my calculations respectively, if that helps.

Screen Shot 2015-11-22 at 18.04.54.png

Reply 1

ghostwalker

Original post by aymanzayedmannan

...

If the stone is moving parallel to OB then the velocity vector will be in the same direction as OB, and they will have the same gradient, which is....

Reply 2

Ayman!

Original post by ghostwalker

If the stone is moving parallel to OB then the velocity vector will be in the same direction as OB, and they will have the same gradient, which is....

It should be 21/20, right? But my approach was a little different. I considered the angle AOB to be the same as the angle between the horizontal velocity and the vertical velocity at that point. I then found the vertical velocity using Pythagoras and used a SUVAT equation to find time. Could you tell me why this hasn't worked?

Reply 3

Zacken

I've recently done this question as well, the mark scheme's approach was substantially different to mine.

I found the vector OB in the form

ai + bj

Then,

v = ci + dj

, so since they are parallel:

v = m\textbf{OB}

for some integer

m

.

Then using SUVAT for the vertical direction keeping in mind that

a = mc

should be enough to get you time.

Reply 4

Ayman!

Original post by Zacken

I've recently done this question as well, the mark scheme's approach was substantially different to mine.

I found the vector OB in the form

ai + bj

Then,

v = ci + dj

, so since they are parallel:

v = m\textbf{OB}

for some integer

m

.

Then using SUVAT for the vertical direction keeping in mind that

a = mc

should be enough to get you time.

Ah, a vector approach is always nice to see. Extremely clever, I must say! I used a vector dot product for Jan 2010 for the last projectile question but the mark scheme used some odd trig methods. Would OB just be the displacement vector then?

How is M2 going for you in general? I'm taking it in January as well. The recent papers (especially the IAL ones) seem to be much more difficult than the Solomons and older papers.

Reply 5

Zacken

Original post by aymanzayedmannan

OB would be the displacement vector, yes - you can get

a

by resolving horizontally (use trig to find the angle OB makes with the vertical) and

j

by resolving vertically.

It's going okay, M1-2, S1-2, C1-4, FP1 is going fine but M3 is giving me some hiccups... although now that you've brought up this IAL thing, I'm a little worried - I've left all 2013, 2014, 2015 papers, both IAL and non-IAL as mocks in the run up to the exam. :frown:

Reply 6

ghostwalker

Original post by aymanzayedmannan

It should be 21/20, right? But my approach was a little different. I considered the angle AOB to be the same as the angle between the horizontal velocity and the vertical velocity at that point.

The angle AOB would be the angle between the vertical velocity and the actual velocity for part c.

Reply 7

Ayman!

Original post by Zacken

OB would be the displacement vector, yes - you can get

a

by resolving horizontally (use trig to find the angle OB makes with the vertical) and

j

Someone as clever as you shouldn't run into any issues with challenging papers, so no need to worry! Which part of M3 is troubling you? I'm working through the review exercises in the book at the moment, long way away till my M3 exam. :P

Original post by ghostwalker

The angle AOB would be the angle between the vertical velocity and the actual velocity for part c.

I see my error, thank you so much for the help. :smile:

Reply 8

Zacken

Original post by aymanzayedmannan

Centres of mass. I can do computing their distance from a point or something, but when it comes to adding a particle of mass kM and find the value of k, urgh, can't do that, :tongue: