A cliff diver positions herself on a cliff that angles downwards towards the edg

Question

A cliff diver positions herself on a cliff that angles downwards towards the edge. The length of the top of the cliff is 48.0 m and the angle of the cliff is = 21.0° below the horizontal. The cliff diver runs towards the edge of the cliff with a constant speed, and reaches the edge of the cliff in a time of 5.50 s. After running straight off the edge of the cliff (without jumping up), the diver falls h = 30.0 m before hitting the water.

(a) After leaving the edge of the cliff, how much time does the diver take to get to the water?
s

(b) How far horizontally does the diver travel from the cliff face before hitting the water?
m

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Explanation / Answer

length of the top l = 48 m

initial PE of the diver with respect to the edge = PE = m*g*l*sin21

at the KE = 0.5*m*v^2

from energy conservation

KE = PE

v = sqrt(2*g*l*sin21)

v = sqrt(2*9.8*48*sin21)

v = 18.36 m/s

at the edge

along vertial vy = -v*sin21 = -6.58 m/s

vx = v*cos21 = 17.14 m/s

from equation of motion

y = vy*t + 0.5*g*t^2

-30 = -6.58*t-4.9*t^2

t = 1.89 s   <<<<------answer

part(b)

along horizantal X = vx*t

X = 17.14*1.89

X = 32.4 m <<<<<--------answer

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