SOLUTION: A stone is thrown horizontally at a speed of +5.0m/s off the top of a cliff 78.4m high. a) how long does it take the stone to reach the bottom of the cliff? (answer 4 sec) b)

Algebra ->  Formulas -> SOLUTION: A stone is thrown horizontally at a speed of +5.0m/s off the top of a cliff 78.4m high. a) how long does it take the stone to reach the bottom of the cliff? (answer 4 sec) b)       Log On


   



Question 1164943: A stone is thrown horizontally at a speed of +5.0m/s off the top of a cliff 78.4m high.
a) how long does it take the stone to reach the bottom of the cliff? (answer 4 sec)
b) how far from the base of the cliff does the stone strike the ground? answer 20 m
c) what are the horizontal and vertical componennts of the velocity of the stone before it hits the ground (vyf=-39.2m/s, vx= 5m/s)

Answer by ikleyn(52788) About Me  (Show Source):
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A stone is thrown horizontally at a speed of +5.0m/s off the top of a cliff 78.4m high.
a) how long does it take the stone to reach the bottom of the cliff? (answer 4 sec)
b) how far from the base of the cliff does the stone strike the ground? answer 20 m
c) what are the horizontal and vertical componennts of the velocity of the stone before it hits the ground (vyf=-39.2m/s, vx= 5m/s)
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            From my school years,  I remember the standard mantra solving this classic  Physics problem.


The thrown body participates in two movements.


One movement is horizontal with the horizontal velocity  v = 5.0 m/s = constant.

The other movement is vertical uniformly accelerated with the vertical acceleration of g = 9.81 m/s6^2.


The time to get the bottom of the cliff is determined from the equation

    %28g%2At%5E2%29%2F2 = H,   or  %289.81%2At%5E2%29%2F2 = 78.4 m,

which gives

    t%5E2 = %282%2AH%29%2Fg = %282%2A78.4%29%2F9.81 = 15.984;  t = sqrt%2815.984%29 = 4 seconds (approximately).


During this time, the horizontal distance is  d = v*t = 5.0 * 4 = 20 m, approximately.


Horizontal component of the final velocity is v = 5.0 m (the given constant).


Vertical component of the final velocity is  v%5Bvert%5D = -g*t = -9.81*4 = -39.2 m/s.

Solved and explained, in all details.