Question

Optimization help

Answer 1

Jeep can travel at 48 km/hr in sand and 80 km/hr on paved road. find shortest time.

Answer 2

Can someone show me how to do this i am not sure im pretty sure dx/dt=80 and dy/dt=48

Answer 3

would i use the Pythagorean theorm

Answer 4

can i please get some help

Answer 5

i need help with how to start it i thought i could use sign or something but im lost

Answer 6

No one can help me? :(

Answer 7

@nincompoop Can you help please? I don't remember how to do this

Answer 8

is it a right-angled triangle that u have drawn? If so, first figure out distance of the direct path to the power plant.

This Q has nothing to do with dx/dt or dy/dt.

Answer 9

it is not a right angled triangle its just supposed to be different paths.

Answer 10

help?

Answer 11

if it is not right-angled triangle then you need to know the positions of jeep and power plant and where the desert and paved road are in order to perform the optimization.

Answer 12

yes its in the picture and i see that but what i want to know is how would i set this up i knw i need one common variable. would i use the Pythagorean theorm

Answer 13

total travel time = time on sand + time on paved road
= distance on sand/48 + distance on paved road/80

Since distance on sand and on paved road are related by Pyth theoren, you can set that up with a single variable. Then differentiate total travel time against that variable to find the max/min

Without looking at the exact picture, that is all I can say.

Answer 14

you cant see the picture thats on here?

Answer 15

Write down the equation which represents the time and find the minimum of it.
\[t = \frac{s_1}{v_1} + \frac{s_2}{v_2}\]

Answer 16

But how does that work for the path that goes through sand and paved road?

Answer 17

Velocities are given, you need to describe the s_1 and s_2 via 1 variable. There are many ways to do so (using angles and trigonometry, pythagoras, even vectors are possible).

Answer 18

I am sorry I am lost. Would this be a way to find the point?
\[\tan \frac{ 32 }{ 16 }\]