# Inclined plane problem

1. Sep 27, 2010

### The legend

1. The problem statement, all variables and given/known data

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

2. Relevant equations

Newtons equations of motion
Projectile equations

3. 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)

2. Sep 27, 2010

### 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, tfinal=t1+t2. What mathematical technique can you use to maximize a value with respect to a certain variable?

Last edited: Sep 28, 2010
3. Sep 28, 2010

### The legend

Oh Yeah!! I got it!
Thanks a lot !