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
Answers
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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