Question

Question For IIT aspirants

A stone is thrown from ground level over horizontal ground. It just clears three walls, the successive distances between them being r and 2r. The inner wall is 15/7 times as high as the outer walls which are equal in height. The total horizontal range is nr, where n is an integer. Find n
a. 2
b. 3
c. 4
d. 5​

Answer 1

Answer:

Question

A stone is thrown from ground level over horizontal ground. It just clears three walls, the successive distances between them being r and 2r. The inner wall is 15/7 times as high as the outer walls which are equal in height. The total horizontal range is nr, where n is an integer. Find n.

Solution

Let us just assume that both the outer walls are equal in height say

h

h and they are at equal distance

x

x from the end points of the parabolic trajectory as can be shown below in the figure.

Now equation of the parabola is

y=bx-cx 2 (1)

y=0 +at

x=nr=R

where

R

R is the range of the parabola.

Putting these values in equation (1) we get

b=cnr (2)

Now the range

R

R of the parabola is

R=a+r+2r+a=nr

This gives

a=(n−3)r2 (3)

The trajectory of the stone passes through the top of the three walls whose coordinates are

(a,h),(a+r,157h),(a+3r,h)

Using these co-ordinates in equation 1 we get

h=ab−ca2

157h=b(a+r)−c(a+r)2 (5)

h=b(a+3r)−c(a+3r)2 (6)

After combining (2), (3), (4), (5) and (6) and solving them we get n = 4.

Explanation:

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