Question

A rock dropped from a cliff covers one-third of its total distance to the ground in the last second of its fall. Air resistance is negligible. How high is the cliff?

Answer 1

distance covered inlast sec. is v+1/2g=v+5=1/3h;
v=([2h/g]^1/2 -1)g;
v^2=(h/5+1-2[h/5]^1/2)g^2;
solve these and eliminatte v you get h

Answer 2

@ashwinjohn3 what would be the answer in your opinion?

Answer 3

ur answer will b 148.48 m

Answer 4

can i explain my work

Answer 5

ok use the equation.......
Diplacement @ nth second=u+ a(2n-1)/2

Answer 6

no

Answer 7

i wanna use the equation\[h=ut+ \frac{ 1 }{ 2 } g t ^{2}\]

Answer 8

for full height u=0

Answer 9

and my equation become
\[h=0+\frac{ 1 }{ 2 } g t ^{2}\]

Answer 10

\[h=\frac{ 1 }{ 2 } \times 10 \times t ^{2}=5 \times t ^{2}\]

Answer 11

its my 1st equation

Answer 12

now i wanna write another equation for 1st 2/3 h height

Answer 13

\[\frac{ 2 }{ 3 }h=ut+\frac{ 1 }{ 2 } \times g t ^{2}=\frac{ 1 }{ 2 } \times 10 \times (t-1)^{2}\]

Answer 14

now u hv to solve these 2 equation to get time t and then u will get the height h

Answer 15

You will get two values for t, but one of them will be less than 1 second, making it invalid, as you can see from the question "covers one-third of its total distance to the ground in the *****last second***** of its fall"

Solve the two equations shamim gave you, by substituting the first one into the second, then solve for t. The second equation comes from the fact that, if it covers one third of the total distance in the last second, then it must cover the initial 2/3rds of the total distance in (t-1) seconds.

\[h = \frac{ 1 }{ 2} g t ^{2}\]
\[\frac{ 2 }{ 3} h = \frac{ 1 }{ 2} g (t - 1) ^{2}\]

Answer 16

Say the height of the cliff is H,
time take for fall is T, and
g is the acceleration of freefall.

\[H=\frac{ 1 }{ 2 }gT ^{2}\] --- (1)
\[\frac{ 2 }{3} H=\frac{ 1 }{ 2 }g(T -1)^{2}\] --- (2)

Solving you will get 2 answer for T:
0.551 s and 5.45 s
But T>1,
Hence H = 146 m