IIT JEE 2006 Sample Question Paper

Passage 5

The Sun's path from sunrise to sunset varies with the time of year. A student performed the following experiments on three clear, sunny days at three- or four-month intervals throughout the course of a year to study the path of the Sun through the sky.

Experiment 1

At a chosen Northern Hemisphere location, the student placed a stick vertically into the ground so that 1 meter of its length was left above ground. The student knew that the length of the shadow was related to the height of the Sun above the horizon and that the shadow would point away from the direction of the Sun. The length in meters (m) and direction of the shadow cast by the stick were measured one hour after sunrise (Shadow A), at mid-morning (B), at noon (C), at mid-afternoon (D), and one hour before sunset (E) on each of the three days. The direction of each shadow was determined by placing a magnetic compass at the base of the stick and aligning the north arrow with the north mark on the compass. The direction of each shadow was then determined by a comparison with the compass face markings. The results are recorded in Table 1.

Table 1:

Shadow	Day 1		Day 2		Day 3
	Length (m)	Shadow direction	Length (m)	Shadow direction	Length (m)	Shadow direction
A	5.0	SW	8.6	NW	6.8	W
B	1.2	W	2.9	NNW	1.7	NW
C	0.3	N	2.3	N	0.9	N
D	1.2	E	3.0	NNE	1.8	NE
E	5.0	SE	8.6	NE	6.9	E

Experiment 2

The following year, the student repeated Experiment 1 at a chosen location in the Southern Hemisphere. The results are in Table 2.

Table 2:

Shadow	Day 1		Day 2		Day 3
	Length (m)	Shadow direction	Length (m)	Shadow direction	Length (m)	Shadow direction
A	9.0	SW	5.0	NW	6.9	W
B	3.2	SSW	1.1	W	1.8	SW
C	2.5	S	0.3	S	1.0	S
D	3.2	SSE	1.1	E	1.8	SE
E	9.1	SE	5.0	NE	6.9	E

Q. 21 Which of the following was a constant in both experiments?

1. Length of vertical stick exposed
2. Shadow direction
3. Day of the year
4. Shadow length

Q. 22 If the experiments were repeated after pounding the stick farther into the ground so that only 0.5 m was exposed, how would this affect the shadow lengths?

1. They would be twice as long as those in the original experiments.
2. They would be one-and-one-half times as long as those in the original experiments.
3. They would be one-half as long as those in the original experiments.
4. They would be one-fourth as long as those in the original experiments.

Q. 23 Which of the following graphs best represents the relationship between the length of the stick's shadow and the time of day?

Q. 24 When the Sun is at an altitude 45o above the horizon, a vertical object will cast a shadow with a length equal to the object's height. Which of the following days included a measurement taken when the Sun was at an altitude of 45o ?

1. Day 1 in Experiment 1
2. Day 1 in Experiment 2
3. Day 2 in Experiment 1
4. Day 3 in Experiment 2

Q. 25 Which of the following statements is best supported by the direction of Shadow A on each of the three days in Experiment 1?

1. The direction of sunrise along the horizon varies throughout the year.
2. Shadows never point due south in the Northern Hemisphere.
3. Shadows never point due north in the Northern Hemisphere.
4. The Sun's brightness varies throughout the year.

Q. 26 Based on the shadow directions in these experiments, which of the following best describes the difference between the apparent path of the Sun as seen from the observation points in the Northern and Southern Hemispheres?

1. The Sun travels a more southerly path in the Southern Hemisphere than in the Northern Hemisphere.
2. The Sun travels a more northerly path in the Southern Hemisphere than in the Northern Hemisphere.
3. The Sun rises in the East and sets in the West in the Northern Hemisphere, but the opposite is true in the Southern Hemisphere.
4. The Sun rises in the West and sets in the East in the Northern Hemisphere, but the opposite is true in the Southern Hemisphere.