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Answer:
Distance between the van and Morristown is changing at the rate of 13.22 miles per hour.
Step-by-step explanation:
From the figure attached,
Van starts from C (City of Morristown), reaches the point A 191 miles due North and then it travels with a speed of 25 miles per hour due East from A towards B.
We have to calculate the rate of change of distance BC, when the van reaches point B which is 119 miles away from A.
By Pythagoras theorem in the triangle ABC,
Distance AC is constant equal to 191 mi.
By differentiating the equation with respect to time 't'
Since BC² = (119)²+ (191)²
BC = √50642 = 225.04 miles
From the differential equation,
[Since
miles per hour]
miles per hour
Therefore, distance between the van and Morristown is changing at the rate of 13.22 miles per hour.
