# Homework Help: Projectile motion off a cliff at an angle (help )

1. Feb 11, 2010

### Wraith09

Projectile motion off a cliff at an angle (help plz)

Hi all,

I am new to the forum, 1st year chemical engineering student. I am struggling with this problem:

1. The problem statement, all variables and given/known data

A stone is thrown at an angle of 37' from the top of a cliff which is 40m above the surface of a lake. The stone hits the lake's surface at a point which is 75m horizontally from the base of the cliff. Find the total time of flight of the stone:

MCQ:

a) 4.44s
b) 4.00s
c) 3.80s
d) 3.60s
e) 3.40s

2. Relevant equations

sy = syo + vyot + 0.5ayt2

3. The attempt at a solution

I drew a free body diagram for the statement incl. a triangle with an angle of 37'. The hypotenuse of the triangle is speed (vo) and its two sides are vox and voy. I also calculated Sy using Cosө = adj / hyp and then sinө = opp / hyp to get 56.516m

To find voy: sin 37' = voy / vo
voy = vo sin 37'

To find vox: cos 37' = vox / vo
vox = vo cos 37'

I relate vox with dislpacement x over a certain period through the eq:

vox = x / t
x = (vox) t

I relate motion along the y-axis to the displacement in this direction over a certain period via the eq:

y = (v0y)t - 0.5at2

Sustituting eqs: vo = x / t
vo cos 37' = x / t
vo = x / (cos 37') t

Substituting eqs: sy = soy + voyt + 0.5(a)t2

sy = soy +(x / (cos 37')t) (sin37') t + 0.5(a)t2

57.516m = 40 + 75 tan37' +0.5(-9.8m.s-2)t2

t2 = 8.16
t = 2.85s

That is the answer I get... which is wrong as its not listed in the MC's

2. Feb 11, 2010

### rl.bhat

Re: Projectile motion off a cliff at an angle (help plz)

Hi Wraith09, welcome to PF.
Measure the displacement from the starting point. So so(y) = 0 and s(y) = -40 m.

3. Feb 11, 2010

### Wraith09

Re: Projectile motion off a cliff at an angle (help plz)

Thank you, thats the one thing I missed!