Optimization car travel problem

Click For Summary
SUMMARY

The optimization problem involves calculating the quickest route for an amphibian vehicle traveling from point A to point C, with point B as a reference. Point A is 20 miles east of point B on land, while point C is 12 miles north of point B on water. The vehicle travels at 52 mph on land and 20 mph on water, making land travel 2.6 times faster. The goal is to determine the optimal point where the vehicle should transition from land to water to minimize travel time.

PREREQUISITES
  • Understanding of basic calculus concepts, particularly optimization.
  • Familiarity with the principles of speed, distance, and time calculations.
  • Knowledge of triangle geometry and area minimization techniques.
  • Ability to interpret mathematical problems and apply relevant formulas.
NEXT STEPS
  • Study optimization techniques in calculus, focusing on finding minimum values.
  • Learn about the application of the Pythagorean theorem in real-world problems.
  • Explore speed, distance, and time relationships in physics.
  • Review examples of similar optimization problems in calculus textbooks or online resources.
USEFUL FOR

Students in mathematics or engineering fields, educators teaching optimization methods, and anyone interested in solving real-world problems involving speed and distance calculations.

Black_Hole???
Messages
36
Reaction score
0
I have been working on this problem for 30 min and can;t seem to get anywhere.


Question

You have a amphibian vehicle which can travel 20 mph on the water and 52 mph on the land. You must find the quickest point from point A to C.

-A is 20 Miles east of point B and is all land.
-C is 12 miles north of point B and is all water.

-Calculate the minimum time.



My thinking

At the moment i can only think so find where the area of the triangle has minimum area. Because traveling in water is hurts the time when going on land is 2.6 times faster.

If anyone has any ideas to this problem that be great. Ill keep working on it.
 
Physics news on Phys.org
anyone have any incite?
 
Refresh
 

Similar threads

Find the Speed of a Car Approaching at 190mph: Optimization Problem
  • · Replies 3 ·
Replies
3
Views
2K
The time it takes this thing to travel across 3 points
  • · Replies 1 ·
Replies
1
Views
2K
Finding Arc Length in Optimization Problem
  • · Replies 2 ·
Replies
2
Views
3K
Optimization and related rates trig.
  • · Replies 6 ·
Replies
6
Views
6K
Single variable optimization problem
  • · Replies 3 ·
Replies
3
Views
5K
Optimizing Distribution of Goods with Discount Rate: A Simple Problem
  • · Replies 2 ·
Replies
2
Views
1K
Related rates problem - kinda stuck on this one
  • · Replies 22 ·
Replies
22
Views
4K
High School Does the Bernouli Effect Work On Cars?
  • · Replies 8 ·
Replies
8
Views
3K
Anyone know how to calculate wear & tear on car for travel?
  • · Replies 13 ·
Replies
13
Views
9K
Graduate Optimal Size of Rocket Engine Nozzle for Vacuum Performance
  • · Replies 26 ·
Replies
26
Views
3K