(a)
To find: The function that models the time needed by the man for the trip.
The function that models the time taken by the man is
Given:
Width of river is
Calculation:
Draw the figure according to given situation in the question as shown below.
Figure (1)
In the Figure (1)
The man reaches at point
Width of river
Total time of the trip is sum of time taken to cross the river and time taken to walk the remaining distance.
Let time taken to cross the river be
Total time
The formula to calculate
Distance travelled by the boat is
Apply Pythagorean Theorem in triangle
Substitute
Take square root of above equation.
Substitute
The formula to calculate
Substitute 5 for
Summarize all the information in the table as shown below.
In Words  In Algebra 
Total time for the trip 

Time taken to cross the river 

Time taken in walking 

Use the information in the table and model the function.
Thus, the function that models the time taken by the man is
(b)
To find: The point at which the man should reach to minimize the time of trip.
The distance is
The function that models the time as calculated in part(a) is
Sketch the graph of the function as shown below.
Figure (2)
Observe from the graph that function attains a minimum value when x is
Thus, man should land at distance of