Wall Shadow Area Dependence on Dimensions
The area of the shadow cast by a vertical wall depends on how the wall's dimensions interact with the sunlight's direction and angle.
Shadow Formation Factors
- Sun's Elevation: The angle of the sun (given as 45° here) determines how the shadow is cast, affecting its size and shape.
- Wall Dimensions: The primary dimensions influencing the shadow's area on the ground are those projected onto the ground plane.
Relevant Wall Dimensions
For a vertical wall casting a rectangular shadow:
- Height: The wall's vertical height contributes to one dimension of the shadow on the ground.
- Length: The wall's length along the ground (perpendicular to the direction of the shadow's primary spread) determines the other dimension of the rectangular shadow.
Irrelevant Dimension: Thickness
The thickness of the wall is its dimension perpendicular to both its height and its length facing the sun. Since the shadow is formed on the ground surface, the wall's thickness does not affect the calculated area of this shadow. A thin wall and a thick wall of identical height and length would cast shadows of the same area.
Therefore, the area of the shadow does not depend on the wall's thickness.
Important Questions from Geometry (Notes)
- Which of the following is not true for a parallelogram?
- A 6 cm long chord of a circle is at a distance of 4 cm from the centre of the circle. Find the distance of 8 cm long chord of the same circle from the centre.
- The length of major axis and coordinate of vertices for the ellipse $3x^2 + 2y^2 = 6$ respectively are:
- If the line through (3, y) and (2, 7) is parallel to the line through (-1, 4) and (0,6), then the value of y is:
- The points (K, 2 – 2K), (-K +1,2K) and (-4-K, 6-2K) are collinear if:
(A) K = $\frac{1}{2}$
(B) K = $-\frac{1}{2}$
(C) K = $\frac{3}{2}$
(D) K = -1
(E) K = 1
Choose the correct answer from the options given below:
