Proportion: a pebble is dropped...

B

bumblebee123

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I've been trying to figure this question out for a while, but I just can't get the right answer. Can anyone help?

Question: a pebble is dropped from the edge of a cliff. The edge of the cliff is 250 metres above the sea. After t seconds, the pebble has fallen a distance of x metres.

x is directly proportional to t^2

when t = 2, x = 19.6

a) find an equation connecting x and t: I managed to do this, the answer was x = 4.9 t^2

b) find the value of x when t = 5: I found this to be 122.5, which was also correct

c) find out how long the pebble takes to fall the final 73.6m before landing in the sea

This is where I get stuck. Here's what I've been doing: 73.6 = 4.9 t^2

15.02.... = t^2

t = sqrt 15.02....

t = 3.875617133

The answer is 1 1/7 seconds

can anyone explain where I'm going wrong? any help would be really appreciated :)
 
What you've done is find the time taken to fall 73.6m from the top of the cliff ie the first 73.6m

The question asks you to "find out how long the pebble takes to fall the final 73.6m before landing in the sea".

Note that the cliff is 250m high (given in the question).

So, to find the time taken to fall the final 73.6m you'll need to find the difference in the times taken to fall the full 250 m and the time taken to fall to a point 73.6 m from the bottom (how far down from the top is that?) Remember x is the distance the pebble has fallen, not the distance from the bottom (ie not the height). The answer 1 1/7 seconds is correct. See if you can get it.

(BTW the reason why the time taken for the final 73.6m (1 1/7 seconds) is less than the time taken for the first 73.6m (your 3.8756...the figure you calculated) is because the pebble is accelerating due to gravity ie it is moving faster, so will take less time to fall the same distance.)
 
Harry_the_cat said:
What you've done is find the time taken to fall 73.6m from the top of the cliff ie the first 73.6m

The question asks you to "find out how long the pebble takes to fall the final 73.6m before landing in the sea".

Note that the cliff is 250m high (given in the question).

So, to find the time taken to fall the final 73.6m you'll need to find the difference in the times taken to fall the full 250 m and the time taken to fall to a point 73.6 m from the bottom (how far down from the top is that?) Remember x is the distance the pebble has fallen, not the distance from the bottom (ie not the height). The answer 1 1/7 seconds is correct. See if you can get it.

(BTW the reason why the time taken for the final 73.6m (1 1/7 seconds) is less than the time taken for the first 73.6m (your 3.8756...the figure you calculated) is because the pebble is accelerating due to gravity ie it is moving faster, so will take less time to fall the same distance.)
Click to expand...

time taken to fall from 250m = 4.9 t^2
t = 7.142857

250m - 73.6m= 176.4 m

time taken from 176.4m = 4.9 t^2
t = 6 seconds

7.143857 - 6 = 1 1/7 seconds

thanks, this makes more sense! :)
 
Jomo said:
I will not help until you put units with those equations!
Click to expand...

time taken to fall from 250metres
250 metres = 4.9 t^2
t = 7.142857 seconds

250metres - 73.6metres= 176.4 metres

time taken from 176.4metres
176. 4 metres = 4.9 t^2
t = 6 seconds

7.143857 seconds - 6 seconds= 1 1/7 seconds
 
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