1. ## Kinematics/Vectors

__________________

The unit vectors $\displaystyle \bold{i}$ and $\displaystyle \bold{j}$ lie in a vertical plane, $\displaystyle \bold{i}$ being horizontal and $\displaystyle \bold{j}$ vertical. A ball of mass $\displaystyle 0.1 kg$ is hit by a bat which gives it an impulse of $\displaystyle (3.5 \bold{i} + 3 \bold{j}) Ns$. The velocity of the ball immediately after being hit is $\displaystyle (10 \bold{i} + 25 \bold{j}) ms^{-1}$.
(a) Find the velocity of the ball immediately before it is hit.

In the subsequent motion the ball is modelled as a particle moving freely under gravity. When it is hit the ball is $\displaystyle 1 m$ above horizontal ground.
(b) Find the greatest height of the ball above the ground in the subsequent motion.

The ball is caught when it is again $\displaystyle 1 m$ above the ground.
(c) Find the distance from the point where the ball is hit to the point where it is caught.

2. the formula of impulse is:

Ft = mv - mu
where,
Ft= impulse
m = mass
v=final velocity
u = initial velocity