A student stands at the edge of a cliff and throws a stone horizontally over the

Question

A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of vi = 17.9 m/s. The cliff is h = 53.5 m above a body of water as shown in the figure below.

(a) 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?

(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

g = 9.8 m/s2

no acceleration from gravity

constant velocity motion

(d) What is the appropriate analysis model for the horizontal motion of the stone? (Select all that apply.)

free fall motion

g = 9.8 m/s2

g = 9.8 m/s2

constant velocity in the horizontal direction

no acceleration from gravity

(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.)

(f) Write symbolic equations for the position of the stone as a function of time. (Use the following as necessary: vix, g, h and t.)

(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?

Explanation / Answer

a)
xi = 0 m and yi = h = 53.5 m
b)
Initial velocity vi = 17.9 m/s i^
hence vix = 17.9 m/s
viy = 0 m/s
c)
In vertical direction, there is free fall motion
i.e. g = -9.8 m/s^2
d)
In horizontal direction, the velocity is constant.
e)
vx = vi
vy = -g*t = -9.8*t
f)
xf = vi*t
yf = -0.5*g*t^2
g)
T = sqrt(2h/g)

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