Need help with applied maths question for test tommorow

MannyFagnet

(a) A particle of mass 4 kg moves under a force: F = 6t^2i - tj - 4k in Newtons.
Assuming that the particle is initially at the origin with velocity v = i + k in m/s, find its position after 1s.

(b) A ball of mass m travels with velocity 3 m/s and collides with a second ball with mass 2m at rest. After the collision the 2m ball moves with speed 1 m/s in a direction 60degrees to the original direction of the ball m.
(i) What is the final velocity of the ball m ?
(ii) What is the angle between the paths of the two balls after the collision ?

Dont have a clue how to do it so please explain if you know how to thanks !

RolandIRL

MannyFagnet wrote: »

(a) A particle of mass 4 kg moves under a force: F = 6t^2i - tj - 4k in Newtons.
Assuming that the particle is initially at the origin with velocity v = i + k in m/s, find its position after 1s.

(b) A ball of mass m travels with velocity 3 m/s and collides with a second ball with mass 2m at rest. After the collision the 2m ball moves with speed 1 m/s in a direction 60degrees to the original direction of the ball m.
(i) What is the final velocity of the ball m ?
(ii) What is the angle between the paths of the two balls after the collision ?

Dont have a clue how to do it so please explain if you know how to thanks !

For part (a), use F=ma to find the acceleration in terms of t. Then write a as dv/dt (rate of change of velocity), integrate wrt t, use your initial condition (velocity at origin) to find out the constants of integration (in each of the unit vector directions i,j,k). You now have velocity as a function of time, so set t=1 to get your answer.

For part (b), use conservation of momentum to solve it. Break it down into vertical and horizontal components eg after collision, the 2m ball has a horizontal component of v*cos60 and a vertical component of v*sin60 where v is the absolute velocity of the 2m ball. Draw out the diagram and make sure you use the correct signs for the vertical components of each of the balls.

If you're still having trouble or wanna check your answers, send me a PM and I'll go into further detail. I'll be on boards for a couple of hours now, but probably won't be on til after 11am or so tomorrow if your exam is on in the morning.