Imagine the falcons fury was put on mars. How far could you see from the top of the ride on mars?

Question

Trigonometric ratios 

Answer 1

Hi Jesse,

 

Suppose your eyes are exactly level with the top of Falcon's Fury, 102 meters above the surface of Mars.  In the distance, there is a last bit of ground you can see before the curvature of Mars' surface hides the rest of the surface.  At the last visible point, the line of sight is tangent to the surface (otherwise, you could raise your eyes a bit and still see some ground).

 

So, we have a tangent to the surface of Mars that ends at a spot 102 meters above Mars.  We will solve for the length of that tangent, which is the distance between your eyes and that last bit of ground that you can see. 

 

Ok, let's call that tangent point T, the top of Falcon's fury F, and the center of Mars C.  The tangent TF is perpendicular to the radius CT.  The radius, of course, being 3,390 km, or 3,390,000 meters.  The line CF is 102 meters longer, due to the height of Falcon's Fury, giving it a length of 3,390,102 meters.  And so, we have a right triangle with T being the right angle and CF being the hypotenuse. 

 

Applying the Pythagorean theorem, we have 3,390,000^2 + TF^2 = 3,390,102^2.  Solving, we have

 

TF^2 = 691570404

TF = 26298 meters = 26.30 km.

 

So you can see 26.3 km

 

Interestingly, if Mars were absolutely perfectly spherical, and you were to set out to walk from the base of Falcon's Fury to T, the distance would be slightly different, as you are walking along a curved surface, not along the straight line segment from F to T.  I can solve that problem for you if you care, but I think we've answered the question you posed.

 

I hope that helps.

 

Regards,

Mike N.