A student stands at the edge of a cliff and throws a stone horizontally over the
ID: 2168493 • Letter: A
Question
A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of vi = 18.2 m/s. The cliff is h = 55.0 ma) What are the coordinates of the initial position of the stone? (Do not assume that the student is the point of origin.)
xi = m
yi = m
(b) What are the components of the initial velocity of the stone?
vix = m/s
viy = m/s
(c) What is the appropriate analysis model for the vertical motion of the stone? (Select all that apply.)
g = ?9.8 m/s2 free fall motion constant velocity motion no acceleration from gravity g = 9.8 m/s2
(d) What is the appropriate analysis model for the horizontal motion of the stone? (Select all that apply.)
g = ?9.8 m/s2 g = 9.8 m/s2 free fall motion no acceleration from gravity constant velocity in the horizontal direction
(e) Write symbolic equations for the x and y components of the velocity of the stone as a function of time. (Use the following as necessary: vix, g, and t.)
vfx =
vfy =
(f) Write symbolic equations for the position of the stone as a function of time. (Use the following as necessary: vix, g and t.)
xf =
yf =
(g) How long after being released does the stone strike the water below the cliff?
(h) With what speed and angle of impact does the stone land?
speed m/s
direction
Explanation / Answer
As is customary, we ignore air resistance in this kind of problem. The horizontal velocity of the stone is irrelevant for purposes of determining when the stone hits the ground. It's the same as a stone just dropped off the cliff. Use the distance formula d = 1/2 * a * t^2 + v0*t + d0 to find out how long it takes to drop. d is equal to 68m of course, and a is the acceleration of gravity, about 10m/sec^2. You will be able to find the vertical component of velocity by the formula v = a*t + v0 The horizontal velocity is assumed to be constant at 14 m/S, and when you know the vertical component of velocity, you can apply trigonometery, and take an arc tangent to get an angle.
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