"DISTANCE BETWEEN TWO CARS A car leaves an intersection traveling west. Its position 4 sec later is 20 ft from the intersection. At the same time, another car leaves the same intersection heading north so that its position t sec later is t² + 2t ft from the intersection. If the speed of the first car 4 sec after leaving the intersection is 9 ft /sec, find the rate at which the distance between the two cars is changing at that instant of time."

You are standing 12 feet away from a balloon launcher that will release a balloon vertically up into the air at a raise of 2 ft/sec. When the balloon is 10 feet up in the air, at what rate is the angle changing between the horizontal and the line of sight?

A boat is sailing at a rate of 10 feet per second away from an observer 5 feet above the boat. How fast is the angle from the observer to the boat changing when the boat is a horizontal distance of 30 feet away from the observer?

An aireraft flies at a constant height along a straight path of 8 km above the ground. The angle of elevation from a fixed point on the ground to the aireraft is marked as x radians, which varies with time. The horizontal distance along the ground of the aircraft from the fixed point is marked as y km. The aircraft is flying at a constant speed of 500 km/h. Find the rate of change of x, in radian per hour, when x is radians ? 8 km