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Two cars start moving from the same point. One travels north at 40 km/h, and the other travels east at 30 km/h. At what rate is the distance between the cars increasing two hours later?
To solve the problem, complete the following steps.
1. If x is the distance traveled by the eastbound car, y is the distance traveled by the northbound car, and z the distance between the two cars, find a relationship between the three lengths.
2. Because the three distances are changing in time, they are functions of t. Differentiate for t the relation obtained above.
3. Using the relation obtained in 2, solve for z'(2).
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