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

by Wraith09
Tags: angle, cliff, motion, projectile
 P: 3 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
 HW Helper P: 4,436 Hi Wraith09, welcome to PF. Measure the displacement from the starting point. So so(y) = 0 and s(y) = -40 m.
 P: 3 Thank you, thats the one thing I missed!

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