Simon suffers an injury at a campsite on the bank of a canal

In summary: Assuming he starts at the bank closest to the hospital, find the location of the land on the opposite bank that he will reach the hospital in the shortest amount of time.In summary, Simon needs to paddle his kayak at 5km/h and pedal his bicycle at 15km/h along the opposite bank in order to reach the hospital in the shortest amount of time.
  • #1
ilii
39
1

Homework Statement


Simon suffers an injury at a campsite on the bank of a canal that is 6sqrt(2) km wide. if he is able to paddle his kayak at 5km/h and pedal a bicycle at 15km/h along the opposite bank, where should be land on the opposite bank to reach the hospital in minimum time?

Homework Equations


assuming Pythagorean theorem , etc.
when you find the equation, then find the derivative and make it = 0 to find max/min
answer

The Attempt at a Solution


I get the hypotenuse to c=6sqrt(2)+x but don't know where to go from here. Help would be appreciated. Diagram included and is an exact copy of the diagram that was provided with the question.
 

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  • #2
ilii said:

Homework Statement


Simon suffers an injury at a campsite on the bank of a canal that is 6sqrt(2) km wide. if he is able to paddle his kayak at 5km/h and pedal a bicycle at 15km/h along the opposite bank, where should be land on the opposite bank to reach the hospital in minimum time?

Homework Equations


assuming Pythagorean theorem , etc.
when you find the equation, then find the derivative and make it = 0 to find max/min
answer

The Attempt at a Solution


I get the hypotenuse to c=6sqrt(2)+x but don't know where to go from here.
What makes you think that is the hypotenuse? What you have is just the sum of the width of the canal and the distance down the other side. In your relevant equations, you list the theorem of Pythagoras. Do you know how to use it to find the hypotenuse of a right triangle?
ilii said:
Help would be appreciated. Diagram included and is an exact copy of the diagram that was provided with the question.
 
  • #3
Simon paddles the hypoteneuse at 5km/h, taking time ##t_p##, then cycles the remaining distance at 15km/h, taking time ##t_c##. Total time ##t = t_p+t_c##, which will be a function of x.
 
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What happened to Simon at the campsite?

Simon suffered an injury while at the campsite on the bank of a canal. It is unclear what exactly happened, but he sustained an injury of some kind.

What kind of injury did Simon sustain?

The type of injury Simon sustained at the campsite on the bank of a canal is unknown. It could range from a minor cut or bruise to a more serious injury.

How did Simon get injured at the campsite?

The exact cause of Simon's injury at the campsite on the bank of a canal is unknown. It could have been due to a slip and fall, an accident with camping equipment, or any number of other possibilities.

Was Simon alone at the campsite when he got injured?

It is unclear whether Simon was alone at the campsite when he got injured. It is possible that he was with friends or family, or he could have been alone.

What should someone do if they suffer an injury at a campsite on the bank of a canal?

If someone sustains an injury at a campsite on the bank of a canal, they should seek medical attention as soon as possible. They should also make sure to properly clean and care for the injury to prevent infection.

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