A rocket is launched so that it rises vertically. A camera is positioned L from the launch pad and it is always pointing towards the rocket. When the rocket is = 1000 ft above the launch pad, its velocity is vo ft/sec. Suppose the necessary rate 5000 ft ho of change of the angle 0 between the camera lens and the ground at that moment is de * rad/sec. Find the velocity vo of the rocket at that moment. dt

15. A hot-air balloon is rising straight up at 5 ft/sec. An observation area is located 80 feet from the take-off point. At the moment that the balloon reaches a height of 60 feet: (a) How fast (in radians/sec) is the angle of elevation from the observation area to the balloon changing? (b) How fast is the distance between the observation area and the balloon changing?

Consider a triangle where two sides have fixed lengths 14 cm and 16 cm. Suppose the two sides are initially at an angle of a = and that they are closing together so that the angle between them is decreasing at a rate of radians per second. What is the rate at which the area of the triangle is decreasing when a = "? 16 cm?/s

Sand is being dumped on a pile in such a way that it always forms a cone whose height Two sides of a triangle are 10 m and 12 m long. The angle between them is increasing at a rate of 0.2 radians/second. How fast is the length of the third side changing when the angle between the sides is 1 radian