Q. A kite is flying at a height of 50 meters. If the angle of elevation from a point on the ground to the kite is 30 degrees, how far is the point from the base of the kite?
Q. A ladder is leaning against a wall. The foot of the ladder is 12 meters away from the wall, and the angle between the ladder and the ground is 60 degrees. What is the height at which the ladder touches the wall?
A.12√3 m
B.6 m
C.12 m
D.24 m
Solution
Using sin(60°) = height/hypotenuse, we find the height = 12 * tan(60°) = 12√3 m.
Q. A length is measured as 100.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a square, what is the uncertainty in the area?
A.1 m²
B.0.5 m²
C.2 m²
D.0.25 m²
Solution
Area = L², so uncertainty in area = 2 * L * (uncertainty in L) = 2 * 100 * 0.5 = 100 m².
Q. A length is measured as 15.0 m with an uncertainty of ±0.2 m. What is the total uncertainty if this length is used in a calculation involving addition with another length of 10.0 m (±0.1 m)?
A.0.3 m
B.0.2 m
C.0.1 m
D.0.4 m
Solution
Total uncertainty = √((0.2)² + (0.1)²) = √(0.04 + 0.01) = √0.05 ≈ 0.224 m.
Q. A length is measured as 15.0 m with an uncertainty of ±0.3 m. If this length is used to calculate the area of a rectangle, what is the maximum possible error in the area calculation?
A.9.0 m²
B.1.5 m²
C.0.9 m²
D.0.45 m²
Solution
Area = length², maximum error = 2 * length * uncertainty = 2 * 15.0 * 0.3 = 9.0 m².
Q. A length is measured as 15.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a rectangle, what is the maximum possible error in the area calculation?
A.15 m²
B.7.5 m²
C.3.75 m²
D.1.5 m²
Solution
Maximum error in area = 2 * length * uncertainty = 2 * 15.0 * 0.5 = 15 m².
Q. A length is measured as 15.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a square, what is the maximum possible error in the area?
A.3.0 m²
B.1.5 m²
C.0.5 m²
D.2.0 m²
Solution
Area = L², maximum error = 2 * L * ΔL = 2 * 15.0 * 0.5 = 15.0 m².
Q. A lens forms a real image of a height 5 cm at a distance of 40 cm from the lens. If the object is placed at 20 cm from the lens, what is the height of the object?
A.2.5 cm
B.5 cm
C.10 cm
D.20 cm
Solution
Using the magnification formula, m = h'/h = -v/u. Here, h' = 5 cm, v = 40 cm, u = -20 cm. Thus, h = (h' * u) / v = (5 * -20) / 40 = 2.5 cm.
Q. A lens forms a real image that is three times the size of the object. If the object is placed 20 cm from the lens, what is the focal length of the lens?
A.10 cm
B.15 cm
C.5 cm
D.20 cm
Solution
Using magnification m = -v/u = 3, we find v = -60 cm and then use the lens formula to find f = 15 cm.
