A football kicks a ball of a cliff overlooking the ocean, the cliff 11.2m above sea level. And she kicks it with initial speed $\displaystyle 10ms^{-1} $ at an angle 30 degrees measured upwards from the horizontal .

Take 9 = $\displaystyle 10ms^{-2} $

1) Assuming that there is no air resistance, how far from the cliff in the horizontal direction

does it hit the ocean?

2) Now suppose that the air resistance can be modelled by a force $\displaystyle f = -kv $ , with k = 0.200kgm^{-1} . Assume that the mass of the football iss 0.2kg.

2a) Write down the equations of motion for the vertical and the horizontal directions.

2b) For motion in the vertical direction, integrate the equation of motion twice to find

a formula for the height of the football as a function of time.

for part 1 I am not sure how to work out the distance, I have resolved the forces into its components

$\displaystyle 10m^{-1} \times cos 30 = 10 \times 1/2 = 5 $

$\displaystyle 10 m^{-1} \times sin 30 $

but how do I work out distance?

and really not sure how to start with on 2a,2b.

any help appreciated.