Question

1.Let θ (in radians) be an acute angle in a right triangle and let x and y, respectively, be the lengths of the sides adjacent to and opposite θ. Suppose also that x and y vary with time. At a certain instant x=1 units and is increasing at 9 unit/s, while y=7 and is decreasing at 19 units/s. How fast is θ changing at that instant?

2.An airplane in Australia is flying at a constant altitude of 2 miles and a constant speed of 600 miles per hour on a straight course that will take it directly over a kangaroo on the ground. How fast is the angle of elevation of the kangaroo's line of sight increasing when the distance from the kangaroo to the plane is 3 miles? Give your answer in radians per minute.

Answer:  .
Hint: The angle of elevation is that angle that the line of sight makes with the horizontal. Construct a triangle representing the situation. Use this to get a equation first involving xx and yy, then differentiate to involve dxdtdxdt and dydtdydt. Think about what it means that the plane is getting closer to the kangaroo.

Answer 1