Projectile motion off a cliff at an angle (help )

  1. 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. jcsd
  3. rl.bhat

    rl.bhat 4,433
    Homework Helper

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

    Thank you, thats the one thing I missed!
     
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