Cody's "Angry LADIES" ! ....not birds....

Cody (yellow) threw a Chocolate \color{#3D99F6}{\text{Chocolate}} horizontally, as shown in the pic with velocity 10 m s 1 10 ms^{-1} for the ladies \color{#D61F06}{\text{ladies}} .

The point from where he throws it is 200 m 200 m above the ground.

The two buildings in the pic are 10 m 10m apart. His chocolate strikes the opposite building (of course the lady doesn't get it) and at the very instant, all ladies close their windows. So his chocolate falls on the ground.

If the chocolate's speed is not affected by the collision with the building, how many times does the chocolate strike the walls of those buildings before it reaches the ground ?

Details and assumptions

Acceleration due to gravity g = 10 m s 2 g=10 ms^{-2}

Cody's chocolate undergoes smooth collisions, it doesn't change the speed by the collision . The only force acting is gravity.

You have to find the number of times chocolate hits the walls , i.e. after those many collisions, before the next one, it will hit the ground.

6 5 4 7

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2 solutions

Aditya Raut
Jun 15, 2014

The displacement along Y axis is 200 m -200m . Initial velocity along Y axis is 0.

S y = 200 = u t g t 2 2 S_y = -200 = ut - \frac{gt^2}{2} ... here u = 0 u=0 and g = 10 g=10

t 2 = 40 t = 40 s e c o n d s t^2 = 40 \implies t =\sqrt{40} seconds

Acceleration along X axis is 0, and initial velocity is 10m/s as given.

Observe that if the walls were not there, the chocolate would have gone S x = u t + a t 2 2 = 10 t = 10 40 m S_x = ut + \frac{at^2}{2} = 10t = 10\sqrt{40} m

Here in this case, according to given conditions of collision, note that if you unfold that path, it is same as the path without walls, hence here , the horizontally Distance covered (not displacement) is same as 10 40 10\sqrt{40}

Thus the chocolate moved horizontally a distance of 10 40 m 10\sqrt{40} m during the motion and as the distance between walls is 10 m 10m , the number of times it's path is changed, i.e. it hits the wall is

10 40 10 = 40 = 6 \lfloor \frac{10\sqrt{40}}{10} \rfloor = \lfloor \sqrt{40} \rfloor = 6

Thus it hits the walls 6 \boxed{6} times and , before it could hit the wall 7th time, it reaches the ground.

Hey, Let's create a new tag, #Cody. Tag these problems with this!

Sagnik Saha - 6 years, 11 months ago

Funny problem! LOL.

Sagnik Saha - 6 years, 11 months ago

To fall 200m , chocolate needs 4 0 \sqrt 40 s. Horizontal distance it travels is 10 4 0 m i t r e n o u n c e s 10 4 0 10 t i m e s t h a t i s 6 t i m e s . 10*\sqrt 40~m \\ \therefore~ it~ renounces~\frac{10*\sqrt 40} {10}~times~that~ is ~6~times. .

Niranjan Khanderia - 6 years, 9 months ago

its x-axis velocity is constant,so it will collide once per second.The time needed to fall in the ground is t=sqrt(2h/g)=sqrt(40),6<t<7.So in time t it will strike the walls 6 times.

1s=10m/10m/s

Georgios Papachatzakis - 6 years, 9 months ago

That's how I did it.

One more way is to imagine that the second building is not there and the chocolate keeps going. If we vertically 'fan fold' this path every 10 meters measured horizontally, we get the path because of the collisions!

So just find the horizontal distance covered (range) and divide it by 10.

r a n g e = 10 × 40 range = 10 \times \sqrt {40} bounces = int(range/10) = 6

Ujjwal Rane - 6 years, 7 months ago

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