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 = 22.0 m/s.The cliff is h = 52.6m above a body of water as shown in the figure below.

a) 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. Indicate the direction of the velocity with the sign of your answer.)

v(fx) =

v(fy) =

b) Write symbolic equations for the position of the stone as a function of time. (Use the following as necessary: vix, g, and t. Indicate the direction of the displacement with the sign of your answer.)

x(f) =

y(f) =

c) How long after being released does the stone strike the water below the cliff?

d) With what speed and angle of impact does the stone land?

Explanation / Answer

a)

vx = vi = 22 m/s

vy = - g * t(negative indicates velocity in downward direction)

b) x = vi t

y = - 0.5 * g * t2 (negative indicates velocity in downward direction)

c) - 52.6 = - 0.5 * g * t2

=> t2 = 10.72

=> t = 3.275 s

So stone srtikes water after 3.275 s of release

d) vx = 22 m/s

vy = -9.81*3.275 = 32.1 m/s

So total speed = sqrt ( 22^2 + 32.1^2) = 38.94 m/s

at an angle tan-(22/32.1) = 34.4 degree towards positive x from negative y direction

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