Related Rates Questions
Related Rates
1. A spectator at an air show is trying to follow the flight of a jet. The jet follows a straight path in front of the observer at 792 km per hour. At its closest approach, the jet passes 600 km in front of the person as in Figure Q1 (b). Find the maximum rate of change of the angle between the spectator’s line of sight and a line perpendicular to the flight path as the jet flies away in radian per hour. 2. How fast is the fluid level inside a vertical cylindrical tank that has a radius of 10 meter drops if the fluid is pumped out at the rate of 3000 l/min?
3. A high speed train is traveling at 2 km/min along a straight track. The train is moving away from a movie camera which is located 0.6 km from the track. The camera keeps turning so as to always point at the front of the train. How fast (in radians per minute) is the camera rotating when the front of the train is 1 km from the camera?
4. Two people start walking from the same point. One walks east at 3km/hr and the other walks northeast at 2km/hr. How fast is the distance between the people changing after 15 minutes?
5. A car is travelling at 100 km/hr due south at a point 0.5km north of an intersection P. A police car is traveling at 80km/hr due to west at a point 0.25km east of intersection P. At that instant, the radar in the police car measures the rate at which the distance between the two cars is changing. What does the radar gun register?
1. A spectator at an air show is trying to follow the flight of a jet. The jet follows a straight path in front of the observer at 792 km per hour. At its closest approach, the jet passes 600 km in front of the person as in Figure Q1 (b). Find the maximum rate of change of the angle between the spectator’s line of sight and a line perpendicular to the flight path as the jet flies away in radian per hour. 2. How fast is the fluid level inside a vertical cylindrical tank that has a radius of 10 meter drops if the fluid is pumped out at the rate of 3000 l/min?
3. A high speed train is traveling at 2 km/min along a straight track. The train is moving away from a movie camera which is located 0.6 km from the track. The camera keeps turning so as to always point at the front of the train. How fast (in radians per minute) is the camera rotating when the front of the train is 1 km from the camera?
4. Two people start walking from the same point. One walks east at 3km/hr and the other walks northeast at 2km/hr. How fast is the distance between the people changing after 15 minutes?
5. A car is travelling at 100 km/hr due south at a point 0.5km north of an intersection P. A police car is traveling at 80km/hr due to west at a point 0.25km east of intersection P. At that instant, the radar in the police car measures the rate at which the distance between the two cars is changing. What does the radar gun register?