Q. A person needs 2000 calories a day and wants to get 15% of their calories from fats. How many grams of fat should they consume (1 gram of fat = 9 calories)? (2000)
A.33 grams
B.40 grams
C.50 grams
D.60 grams
Solution
15% of 2000 calories = 0.15 * 2000 = 300 calories from fats. 300 calories / 9 calories per gram = 33.33 grams, rounded to 33 grams.
Q. A person pushes a box with a force of 30 N, but the box does not move. If the coefficient of static friction is 0.6, what is the maximum static friction force?
A.18 N
B.30 N
C.36 N
D.60 N
Solution
The maximum static friction force is equal to the applied force when the box does not move, which is 30 N.
Q. A person standing 20 meters away from a vertical cliff observes the top of the cliff at an angle of elevation of 75 degrees. What is the height of the cliff?
A.10 m
B.15 m
C.20 m
D.25 m
Solution
Using tan(75°) = height/20, we have height = 20 * tan(75°) ≈ 20 * 3.732 = 74.64 m.
Q. A person standing 40 m away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
A.10 m
B.20 m
C.30 m
D.40 m
Solution
Using tan(30°) = height/40, we have 1/√3 = height/40. Therefore, height = 40/√3 ≈ 23.1 m.
Q. A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building?
Q. A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?
Q. A person standing 50 m away from a building observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building?
A.25 m
B.30 m
C.35 m
D.40 m
Solution
Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.
Q. A person standing 50 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?
Q. A person standing on the ground observes the top of a 40 m high building at an angle of elevation of 60 degrees. How far is he from the building? (2023)
A.20 m
B.30 m
C.40 m
D.50 m
Solution
Using tan(60) = √3, distance = height / tan(60) = 40 / √3 ≈ 23.09 m, which rounds to 30 m.
Q. A person standing on the ground observes the top of a pole at an angle of elevation of 75 degrees. If the pole is 10 m high, how far is the person from the base of the pole? (2023)
Q. A person standing on the ground observes the top of a tree at an angle of elevation of 45 degrees. If the person is 10 meters away from the tree, what is the height of the tree?
A.5 m
B.10 m
C.15 m
D.20 m
Solution
Using tan(45°) = height/10, we have 1 = height/10. Therefore, height = 10 m.
Q. A person walks 4 km in 1 hour and then runs 8 km in 30 minutes. What is the average speed for the entire journey? (2023)
A.8 km/h
B.10 km/h
C.12 km/h
D.14 km/h
Solution
Total distance = 4 km + 8 km = 12 km. Total time = 1 hour + 0.5 hours = 1.5 hours. Average speed = Total distance / Total time = 12 km / 1.5 hours = 8 km/h.
