Question

Oil is leaking out of a tank. The depth of oil in the tank for 60 seconds is shown below. Use the graph to work out an estimate of the rate of decrease of depth, in cm/s, at 10 seconds. You must show your working

Answer 1

Given :  Oil is leaking out of a tank.  The depth of oil in the tank for 60 seconds is shown in graph

To find : rate of decrease of depth, in cm/s, at 10 seconds.

Solution:

Depth  is at y axis

Time is at  x axis

Rate of Decrease of depth    =  d(depth) /d(time)

= dy/dx

dy/dx  = slope of tangent  

rate of decrease of depth, in cm/s, at 10 seconds.  is slope of tangent at 10 secs

Tangent line is shown in graph at 10 sec

From graph  x = 0  , y = 80

x = 24  , y = 28

Slope  = (80 - 28 )/(0 - 24)

= 52/(-24)

= -2.16   cm/s

-ve sign indicates decrease of depth

Hence the rate of decrease of depth, in cm/s, at 10 seconds.  = 2.16 cm/sec

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