What Value of h/H Maximizes Time to Reach the Ground?

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Homework Statement

A body falling from rest from given height H hits an inclined plane in its path at height. As a result of this impact the direction of velocity of the body becomes horizontal. For what value of h/H will body take max time to reach the ground?
ANS) h/H = 1/2

Homework Equations

Newtons equations of motion
Projectile equations

The Attempt at a Solution

v² = u² + 2as
v²= 2 * 10 * (H-h)

now time of flight of projectile from inclined plane
T = 2*v*sinx/g*cosy (x being angle of projection and y angle of incline)
this has to be equal to time of projectile dropped with no initial velocity
T = (2h/g)^1/2

equating and substituting i get the answer to be
h/H = 4/5

(which is not the correct answer)

Please help!

 

[jhae2.718]

You want to find the ratio of h/H such that the total time the object falls is maximized. There are two parts to the problem; both deal with projectile motion.

Since we're dealing with time, we don't care about the x component of position, only the y. For the first part, we know that the body is falling from rest, and that the displacement is H-h. What equation can you use to solve for the time it takes the object to reach this point? (Call it t₁.)

Then, the problem tells us that the object hits an inclined plane, changing the direction of the velocity to the horizontal. What does this tell us about $$v_{0x}$$ and $$v_{0y}$$? (Hint: set the displacement for the second part as h and solve for the time it takes to travel this distance, t₂.)

Once you've solved for these two times, t_final=t₁+t₂. What mathematical technique can you use to maximize a value with respect to a certain variable?

 

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Oh Yeah! I got it!
Thanks a lot !