You are in an open field 72, 0 m away from a straight river a) A toy boat down t

Question

You are in an open field 72, 0 m away from a straight river

a) A toy boat down the river runs at a constant speed. With a laser pistol measure that
the distance between you and the toy boat is 97, 0 m and it decreases with 13cm/s How long time does it
before the play boat will pass the point in the river nearest you?

b) You are now 136, 0 m away from your tent as you have set up 8, 0 m from the river (on the same side as
you are). Before you go back to your tent, you will fill up the water bottle in the river. Which point on the
river should you go to for the total trip to the tent to be as short as possible?

Explanation / Answer

please have rough copy with you, initial case at time 0 ,the situation is a right angled triangle with hypotenus 97.0 and one side 72.0 the other side is the river the shortest distance of boat is 72.0 . other side is 65 initially let velocity of boat along river be v then distance of boat with respect to time t is x= (sqrt{72^2 + (65-vt)^2}) rate of change of distance =13 at t=0 so dx/dt = 13 at t=0 => 65v/95 =13 v=19 time taken = 65/19

draw a straight line which is the river mark points A 8.0 ,B 72.0 away from river , distance between two points =136.0 distancealong river for two points is 136^2 - 64^2 . take a arbitrary point D on river join it with points 8.0 ,72.0 distane = AD + BD , take image of point A about the rver let it be C now on river any for point distace from A is distance from C => distance = CD +BD . now join B to C it intersects river at E which is the required point , because shortest distance from C to B is a st line which is 12.0 along the river from point A

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.