Differential Calculus

Car A moves due East at 30 kph at the same instant car B is moving S \(30^\circ\) E, with a speed of 60 kph. The distance from A to B is 30 km. Find how fast is the distance between them separating after one hour.

A car starting at 12:00 noon travels west at a speed of 30 kph. Another car starting from the same point at 2:00 P.M. travels north at 45 kph. Find how (in kph) fast the two are separating at 4:00 P.M.?

Two railroad tracks are perpendicular to each other. At 12:00 P.M. there is a train at each track approaching the crossing at 50 kph, one being 100 km and the other 150 km away from the crossing. How fast in kph is the distance between the two trains changing at 4:00 P.M.?

Water is running into a hemispherical bowl having a radius of 10 cm at a constant rate of 3 \(cm^3/min\). When the water is x cm. deep, the water level is rising at the rate of 0.0149 cm/min. What is the value of x?

What is the allowable error in measuring the edge of the cube that is intended to hold 8 cu. m., if the error of the computed volume is not to exceed 0.03 cu. m?

A standard cell has an emf "E" of 1.2 volts. If the resistance "R" of the circuit is increasing at the rate of 0.03 ohm/sec, at what rate is the current "I" changing at the instant when the resistance is 6 ohms? Assume Ohm's law E = IR.