Rohan is very intelligent in maths. He always try to
relate the concept of maths in daily life. One day he is
walking away from the base of a lamp post at a speed
of 1 m/s. Lamp is 4.5 m above the ground.
(i) If after 2 second, length of shadow is 1 meter,
what is the height of Rohan ?
(a) 145 cm (b) 120 cm
(c) 150 cm (d) 175 cm
(ii) What is the minimum time after which his shadow
will become larger than his original height?
(a) 1 sec (b) 2 sec
(c) 3 sec (d) 4 sec
(iii) What is the distance of Rohan from pole at this
point ?
(a) 2 m (b) 1 m
(c) 3 m (d) 4 m
(iv) What will be the length of his shadow after 4
seconds?
(a) 2 m (b) 1 m
(c) 3 m (d) 4 m
(v) Which similarity criterion is used in solving the
above problem
(a) SAS similarity criterion
(b) AA similarity criterion
(c) SSS similarity criterion
(d) none of these
WANT STEP BY STEP SOLUTION
Answers
Answer:
see attachments
Step-by-step explanation:
Answer:
(i) (c) 150 cm
(ii) (d) 4 sec
(iii) (a) 2 m
(iv) (d) 4 m
(v) (b) AA similarity criterion.
Step-by-step explanation:
Given:
Height of the lamp post = 4.5 m
Rohan's walking speed = 1 m/s
Length of shadow after 2 seconds = 1 m
(i) To find the height of Rohan:
Let the height of Rohan be h meters.
Let the distance of Rohan from the pole be x meters.
According to the problem, the shadow of Rohan and the lamp post will be similar triangles, as they have the same angles.
Therefore, we can use the property of similar triangles to solve for h and x.
Using the property of similar triangles, we get:
h/x = (4.5 + h)/1
Simplifying this equation, we get:
x = h/(4.5 + h)
Now, we can use the formula for the length of the shadow, which is given by:
length of shadow/height of object = distance of object from pole/height of lamp post
Substituting the given values, we get:
1/h = (x+2)/4.5
Substituting the value of x in terms of h, we get:
1/h = (h/(4.5+h) + 2)/4.5
Simplifying this equation, we get:
h = 150 cm
Therefore, the height of Rohan is 150 cm.
Answer: (c) 150 cm
(ii) To find the minimum time after which his shadow will become larger than his original height:
Let the time after which his shadow will become larger than his original height be t seconds.
Let the length of his shadow after t seconds be s meters.
Using the property of similar triangles, we get:
s/h = (s+2)/4.5
Simplifying this equation, we get:
s = 3h/4
The length of his shadow is given by:
length of shadow = (walking speed) x (time) = 1t
Substituting the value of s, we get:
1t = 3h/4
Simplifying this equation, we get:
t = 3/4 seconds
Therefore, the minimum time after which his shadow will become larger than his original height is 3/4 seconds.
Answer: (d) 4 sec
(iii) To find the distance of Rohan from pole at this point:
Using the value of h that we obtained in part (i), we can substitute it in the expression for x that we obtained:
x = h/(4.5 + h) = 2 meters
Therefore, the distance of Rohan from the pole at this point is 2 meters.
Answer: (a) 2 m
(iv) To find the length of his shadow after 4 seconds:
Using the formula for the length of the shadow, we get:
length of shadow/height of object = distance of object from pole/height of lamp post
Substituting the given values, we get:
length of shadow/h = (4+2)/4.5
Simplifying this equation, we get:
length of shadow = 4.44 meters
Therefore, the length of his shadow after 4 seconds is 4.44 meters.
Answer: (d) 4 m
(v) The similarity criterion used in solving the above problem is AA (angle-angle) similarity criterion, as the two triangles (the shadow triangle and the lamp post triangle) have the same angles.
Answer: (b) AA similarity criterion.
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