You must get from a point P on the straight shore of a lake to a stranded swimmer who is 50 m from a point Q on the shore that is 50 m from you (see figure) If you can swim at a speed of 2 m s and run at a speed of 4 m s, at what point along the shore, x meters from Q, should you stop running and start swimming if you want to reach the swimmer in the minimum time a Find the function T that gives the travel time as a function of x, where 0 x 50 b Find the critical point of T on (0, 50) c Evaluate T at the critical point and the endpoints (x 0 and x 50) to verify that the critical point corresponds to an absolute minimum What is the minimum travel time d Graph the function T to check your work i swim 50 m run 50 50 m

Question: You must get from a point P on the straight shore of a lake to a stranded swimmer who is 50 m from a point

You must get from a point P on the straight shore of a lake to a stranded swimmer who is 50 m from a point Q on the shore that is 50 m from you (see figure). If you can swim at a speed of 2 m/s and run at a speed of 4 m/s, at what point along the shore, x meters from Q, should you stop running and start swimming if you want to reach the swimmer in the minimum time?

i swim 50 m! run 50- х Р х 50 m

a. Find the function T that gives the travel time as a function of x, where 0 ≤ x ≤ 50.

b. Find the critical point of T on (0, 50).

c. Evaluate T at the critical point and the endpoints (x = 0 and x = 50) to verify that the critical point corresponds to an absolute minimum. What is the minimum travel time?

d. Graph the function T to check your work.

i swim 50 m! run 50- 50 m

Step by Step Solution

★★★★★

3.52 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Because distance is rate times time the time will ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Calculus Early Transcendentals Questions!

A small island is 2 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the...

A point P on the rim of a wheel of radius a is initially at the origin. As the wheel rolls to the right along the x-axis, P traces out a curve called a cycloid (see Figure 18). Derive parametric...

An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 6 km east...

Suppose a tour guide has a bus that holds a maximum of 106 people. Assume his profit (in dollars) for taking n pec on a city tour is P(n)=n{53 - 0.5n) - 106_ {Although P is defined only for positive...

You must get from a point P on the straight shore of a lake to a stranded swimmer who is 50 m from a point Q on the shore that is 50 m from you (see figure). Assuming that you can swim at a speed of...

Please answer the following questions. 5. Verify that the function y = cosh 5x satisfies the differential equation y" =5\\/25 + (y')2. [Hint: You need to use the identity cosh r - sinh x = 1.] 6. A...

Please answer these questions 7. You must get from a point A on the straight shore of a lake to a L stranded swimmer who is at the point B in the lake. The shortest distance from B to the shore is BC...

Minimizing Travel Time A woman is on a lake in a rowboat located 1 mi from the closest point P of a straight shoreline (see the accompanying figure). She wishes to get to point Q, 10 mi along the...

12 points) -10 mi A woman is on a lake in a rowboat located one mile from the closest point P of a straight shoreline (see the figure). She wishes to get to a point Q, 10 miles along the shore I mi...

1. (80 points) Demonstrate and Explain: Clearly and thoroughly explain your answers to these questions based on the work you did with your group on labs this week. These questions refer to Lab 12A:...

Choose one stand only either YES or NO. 1. Universalists believe that human rights are universal and applicable to every member of the human race. Should universal human rights be applied to cultures...

Saturated vapor R-134a leaves the evaporator in a heat pump system at 10C, with a steady mass flow rate of 0.1 kg/s. What is the smallest diameter tubing that can be used at this location if the...

8 6 . Gordon was recently diagnosed with multiple sclerosis, a degenerative disease that greatlyimpacts his nervous system. He wishes to ensure a financial legacy for his young children. Hediscusses...

3. What are Auchans long-term prospects and what threats does the company face in its dependence on emerging markets? pg102

(a) Sketch the plane curve with the given vector equation. (b) Find r'(t). (c) Sketch the position vector r(t) and the tangent vector r'(t) for the given value of t. r(t) = e t i + 2t j, t = 0

(a) Sketch the plane curve with the given vector equation. (b) Find r'(t). (c) Sketch the position vector r(t) and the tangent vector r'(t) for the given value of t. r(t) = 4 sin t i - 2 cos t j, t =...

(a) Sketch the plane curve with the given vector equation. (b) Find r'(t). (c) Sketch the position vector r(t) and the tangent vector r'(t) for the given value of t. r(t) = (cos t + 1) i + (sin t -...

6-8, As an Equity analyst you are concerned with what will happen to the required return to Universal Toddler Industries stock as market conditions change. Suppose r_RF=5%, r_M= 12%, and b_UTI=1.4....

QUESTION 14 Which of the following ratios is purely a performance ratio? current ratio times interest earned ratio return on assets ratio debt to assets ratio (debt ratio)

James Corporation is comparing two different capital structures: an all-equity plan (Plan I) and a levered plan (Plan II). Under Plan I, the company would have 144,000 shares of stock outstanding....