📘 related rates

1. **State the problem:** A person 2 meters tall walks away from a streetlight 8 meters high. The shadow lengthens at a rate of $\frac{4}{9}$ meters per second. We need to find the

1. **State the problem:** A hot air balloon is 200 feet horizontally from an observer and ascends at 100 ft/min. We want to find how fast the angle of elevation $\theta$ is changin

1. **State the problem:** We have a conical tank with radius $r$ and height $h=12$ feet. Brine flows in at a rate of $\frac{dV}{dt} = 3$ cubic feet per minute. We want to find how

1. **State the problem:** A ladder 25 feet long leans against a barn. The top slides down at 3 ft/sec. Find how fast the foot moves away when it is 7 feet from the wall. 2. **Ident

1. **State the problem:** A camera is mounted 3000 ft from the base of a rocket launching pad. The rocket rises vertically at 880 ft/s when it is 4000 ft above the pad. We want to

1. **State the problem:** Two carts A and B are connected by a rope 39 ft long passing over a pulley P. The pulley P is 12 ft above point Q on the horizontal surface. Cart A is mov

1. **State the problem:** A kite is flying 100 ft above the ground and moving horizontally at 6 ft/s. We want to find the rate at which the angle $\theta$ between the string and th

1. **State the problem:** We are given two ships, A and B, initially 150 km apart horizontally at noon. Ship A sails south at 20 km/h and ship B sails north at 40 km/h. We want to

1. **Problem statement:** A street light is at the top of a 17 ft pole. A 4 ft tall girl walks away from the pole at 3 ft/sec. We want to find the rate at which the tip of her shad

1. **State the problem:** Water flows from a rectangular reservoir of length 10 m and width 6 m into a cylindrical tank of radius 3 m. The water depth in the reservoir decreases at