Min Time Problem Homework: A to B in Min Time

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Homework Statement



A straight road runs through A. B is 120 km down from the road and 75 km perpendicular to the road. A car travels 100 km/h on road and 50 km/h off road. Find the minimum time required to travel from A to B.

Homework Equations


The Attempt at a Solution



I'm not sure how to start this equation. I have drawn a triangle but not sure what to do next. Any help would be greatly appreciated!
 
Last edited:
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What you have said make pretty much no sense!

"A straight road runs through A. B is 120 km down and 75 km perpendicular." B is 120 km down from what? and 75 km perpencular to what?

Oh, and "minimum time" required to drive any distance requires that we know some speed! What information are you not telling us?
 
I edited my question.

I did have speed in it.
 
If I've understood correctly, I can get from A to B by going 120 km along a road, and then going perpendicular to the road for 75 km.

Suppose I go a distance L along the road, and then head offroad at an angle towards B.

1) What is the distance to B from the point where I leave the road?

2) What is the total time I travel on the road? What is the total time I travel off the road?

Add these two. You now have a function of L. Minimize with respect to L.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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