# Motion in two dimention problem

1. Nov 15, 2012

### Ammar w

1. The problem statement, all variables and given/known data
A projectile is fired from the top of a cliff of height h above the ocean below. The projectile is fired at an angle θ above the horizontal and with an initial speed vi. (a) Find a symbolic expression in terms of the variables vi, g, and θ for the time at which the projectile reaches its maximum height. (b) Using the result of part (a), find an expression for the maximum height hmax above the ocean attained by the projectile in terms of h, vi, g, and θ.

2. Relevant equations

vfy = viy - gt = visinθi - gt

the maximum hight = $\frac{vi^2 (sinθi)^2}{2g}$

3. The attempt at a solution

a)
vfy = viy - gt = visinθi - gt

it reaches the maximum hight when vfy = 0.

=> visinθi - gt = 0

t = $\frac{ visinθi}{g}$

right??

b) hmax = viyt - $\frac{1}{2}$gt2

hmax = visinθi ($\frac{ visinθi}{g}$) - $\frac{1}{2}$g ($\frac{ visinθi}{g}$)2

hmax = ..... how to simplify it??

2. Nov 15, 2012

### tiny-tim

Hi Ammar w!

(btw, there's no need to write θi

there's only one θ, so just write θ ! )

just expand that second bracket!

(and then get some sleep! :zzz:)

btw, if you know the standard constant acceleration equations, you should be able to find one that solves the problem straight away​

3. Nov 15, 2012

### SammyS

Staff Emeritus
Your solution to part a) looks fine.

For part b, what is the height (above the ocean) of the projectile at time t = 0 ? It's h, correct?

So you need to modify the equation, hmax = viyt - $\frac{1}{2}$gt2 to reflect that.