Problem 1 You and a friend are sitting on a cliff, tossing pebbles over the edge

Question

Problem 1 You and a friend are sitting on a cliff, tossing pebbles over the edge, either straight up or straight down, so that they land in the lake below. Your pebble is in free fall for 5 seconds, with a final speed of 30m/s. Which way is the pebble going when it hits the lake? How fast and in what direction did you throw the pebble? When was the pebble at its maximum height, assuming it left your hand at t = 0? What was the pebble's maximum height? How high is the cliff? How much work did the Earth (meaning, the Earth's gravitational force) do on the pebble? Assume the pebble's mass is 0.05kg

Explanation / Answer

a)

the pebble going in "downward"

b)

v=u+g*t

30=u+9.8*5

===> u=-19 m/sec (upward)

c)

v=u+a*t

0=u-g*tmax

==>

tmax=u/g

=19/9.8

=1.94 sec

d)

Hmax=u^2/2*g

=19^2/2*9.8

=18.42 m

e)

time taken, t'=5-2*1.94

t'=1.12 sec

and

height of the cliff, h =u*t'+1/2*g*t^2

=19*1.12+1/2*9.8*1.12^2

=27.43 m

f)

workdone=P.E=m*g*h

=0.05*9.8*27.43

=13.44 J

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