Question 1: The voltage V (volts), current I (amperes), and resistance R (ohms) of an electric circuit like the one shown here are related by the equation V=IR. Suppose that V is increasing at the rate of 3 volt/sec while I is decreasing at rate $\frac{1}{2}$ amp/sec. Let t denote time in seconds. Answer the following questions:

1. What is the value of $\frac{dV}{dt}$?
2. What is the value of $\frac{dI}{dt}$?
3. What equation relates $\frac{dR}{dt}$ to $\frac{dV}{dt}$ and $\frac{dI}{dt}$?
4. Find the rate at which R is changing when V = 8 volts and I = 4 amps. Is R increasing or decreasing?

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Question 3: A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 24ft from the house, the base is moving away at the rate of 21 ft/sec.

1. What is the rate of change of the height of the top of the ladder?
2. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then?
3. At what rate is the angle between the ladder and the ground changing then?

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Question 4: A child flies a kite at a height of 50 ft, the wind carrying the kite horizontally away from the child at a rate of 26 ft/sec. How fast must the child let out the string when the kite is 130 ft away from the child?

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Question 5: A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 8 ft above the bow. The rope is hauled in at the rate of 2 ft/sec. Complete parts (a) and (b).