You are Here: Home >< Maths

# Dynamics mechanics help watch

1. These are the questions below. Basically what i am having trouble with is:
finding time between collisions given force initial speed and colision speed.

how to find maximum range of projectile from height of y0 and optimum angle

for a planet in orbit, at particular time it has r=a and speed=u. what would be energy and angular momentum and what would happen if: u<1, u>1 and u=1/a

thanks!
Spoiler:
Show

1. Train A is moving with speed v_i and sees train B stationary ahead. He puts his brakes on to avoid a collisionand isslowed by force deltaMv where v is speed and M is mass of train A. But train A hits train B with speed v_f. Find the time T between application of brakes and collision.

2a. A man climbs on a mountain of height y_0. The stone is thrown at an angle of 0 to the horizontal . r(t)=x(t)i+y(t)j find x(t) and y(t) and hence trajectory y(x).
b.how far is it thrown if thrown horizontally?
c. Roughly what is the best angle in order to throw the stone as far as possible assuming geight y0 is much larger than max height boy can throw. explain answer briefly?

3a. A planet moves with position r and central force F(r). Derive a formula for velocity in suitable polar coordinates and so write L=lLl and planets KE.
b. if F(r)=-1/r^3 find a formula for total energy E.
c. if r=a then the planets sped u is transverse to position, then express E and L in terms of a and u and so relate dr/dt to r and these constants.
d. describe the motion in cases: u<1, u>1 and u=1/a

thanks!
2. ???
3. (Original post by number23)
???
You've been posting long enough to be aware of the forum guidelines.

Just posting a mass of questions isn't going dispose people to just do them for you. You need to say what problem you're having, what have you been able to do, etc.
4. (Original post by ghostwalker)
You've been posting long enough to be aware of the forum guidelines.

Just posting a mass of questions isn't going dispose people to just do them for you. You need to say what problem you're having, what have you been able to do, etc.
ok thnx ive edited my post
5. (Original post by number23)
ok thnx ive edited my post
For your first one. Apply F=ma, and note that a is dv/dt.

You now have a very simple differential equation.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 15, 2013
Today on TSR

### The most controversial member on TSR?

Who do you think it is...

### Is confrontation required?

Discussions on TSR

• Latest
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE