Suppose oil spills from a ruptured tanker and spreads in a circular pattern. if the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius is 30 m?

Explanation:

As we know that area of the circle at any instant of time is given as

now in order to find the rate of change in area we will have

here we know that

rate of change of radius is given as

radius of the circle is given as

now we have

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initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft