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Q. A person is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and the person is 20 meters away from the tree, what is the height of the tree?

A. 20√3 meters
B. 10√3 meters
C. 30 meters
D. 40 meters

Solution

Height = distance * tan(angle) = 20 * tan(60°) = 20 * √3 meters.

Correct Answer: A — 20√3 meters

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Q. A person is walking at 2 m/s on a train moving at 10 m/s. What is the speed of the person relative to the ground?

A. 2 m/s
B. 8 m/s
C. 10 m/s
D. 12 m/s

Solution

Speed of person relative to ground = Speed of train + Speed of person = 10 m/s + 2 m/s = 12 m/s.

Correct Answer: D — 12 m/s

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Q. A person is walking at 4 km/h in a train moving at 36 km/h. What is the speed of the person relative to the ground?

A. 32 km/h
B. 40 km/h
C. 36 km/h
D. 4 km/h

Solution

Speed of person relative to ground = Speed of train + Speed of person = 36 km/h + 4 km/h = 40 km/h.

Correct Answer: B — 40 km/h

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Q. A person lifts a box of mass 10 kg to a height of 2 m in 4 seconds. What is the power exerted by the person?

A. 50 W
B. 25 W
C. 100 W
D. 75 W

Solution

The work done against gravity is W = mgh = 10 kg * 9.8 m/s² * 2 m = 196 J. Power is P = W/t = 196 J / 4 s = 49 W, approximately 50 W.

Correct Answer: A — 50 W

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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.

Correct Answer: C — 36 N

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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.

Correct Answer: D — 25 m

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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.

Correct Answer: B — 20 m

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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?

A. 20 m
B. 40 m
C. 30 m
D. 10 m

Solution

Height = distance * tan(angle) = 40 * 1 = 40 m.

Correct Answer: B — 40 m

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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?

A. 40√3 meters
B. 20√3 meters
C. 30 meters
D. 50 meters

Solution

Height = distance * tan(angle) = 40 * tan(60°) = 40√3 meters.

Correct Answer: A — 40√3 meters

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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.

Correct Answer: B — 30 m

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Q. A person standing 50 m away from a tree observes the angle of elevation to the top of the tree as 30 degrees. What is the height of the tree?

A. 25 m
B. 50 m
C. 15 m
D. 20 m

Solution

Using tan(30°) = height/distance, we have height = distance * tan(30°) = 50 * (1/√3) = 25 m.

Correct Answer: A — 25 m

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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?

A. 25 meters
B. 50 meters
C. 35 meters
D. 45 meters

Solution

Height = distance * tan(angle) = 50 * tan(45°) = 50 meters.

Correct Answer: B — 50 meters

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Q. A person standing 60 meters away from a tree sees the top of the tree at an angle of elevation of 30 degrees. What is the height of the tree?

A. 20√3 m
B. 30 m
C. 60 m
D. 10 m

Solution

Height = distance * tan(angle) = 60 * (1/√3) = 20√3 m.

Correct Answer: A — 20√3 m

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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.

Correct Answer: B — 10 m

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Q. A person walks at 4 km/h and runs at 10 km/h. If he walks for 30 minutes and then runs for 30 minutes, what is his average speed?

A. 6 km/h
B. 7 km/h
C. 8 km/h
D. 9 km/h

Solution

Total distance = (4 × 0.5) + (10 × 0.5) = 2 + 5 = 7 km. Total time = 1 hour. Average speed = 7 km/h.

Correct Answer: B — 7 km/h

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Q. A person walks at 4 km/h and runs at 10 km/h. If he walks for 30 minutes and then runs for 1 hour, how far does he travel?

A. 7 km
B. 8 km
C. 9 km
D. 10 km

Solution

Distance walked = 4 * 0.5 = 2 km; Distance run = 10 * 1 = 10 km; Total distance = 2 + 10 = 12 km.

Correct Answer: C — 9 km

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Q. A person walks at 4 km/h and runs at 10 km/h. If he walks for 30 minutes and then runs for 30 minutes, how far does he travel?

A. 5 km
B. 7 km
C. 8 km
D. 10 km

Solution

Distance walked = 4 km/h * 0.5 h = 2 km. Distance run = 10 km/h * 0.5 h = 5 km. Total distance = 2 + 5 = 7 km.

Correct Answer: C — 8 km

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Q. A person walks at 4 km/h in a train moving at 36 km/h. What is the speed of the person relative to the ground?

A. 32 km/h
B. 36 km/h
C. 40 km/h
D. 4 km/h

Solution

Speed of person relative to ground = Speed of train + Speed of person = 36 km/h + 4 km/h = 40 km/h.

Correct Answer: C — 40 km/h

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Q. A person walks at 4 km/h in a train moving at 60 km/h. What is the speed of the person relative to the ground?

A. 64 km/h
B. 60 km/h
C. 4 km/h
D. 56 km/h

Solution

Speed of person relative to ground = Speed of train + Speed of person = 60 km/h + 4 km/h = 64 km/h.

Correct Answer: A — 64 km/h

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Q. A person walks at 4 km/h in still water. If the current of the river is 2 km/h, what is the speed of the person relative to the bank when walking upstream?

A. 2 km/h
B. 4 km/h
C. 6 km/h
D. 8 km/h

Solution

Speed upstream = Speed of person - Speed of current = 4 km/h - 2 km/h = 2 km/h.

Correct Answer: A — 2 km/h

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Q. A person walks at 4 km/h on a moving escalator that moves at 2 km/h. What is the speed of the person relative to a stationary observer?

A. 2 km/h
B. 4 km/h
C. 6 km/h
D. 8 km/h

Solution

Speed of person relative to observer = Speed of person + Speed of escalator = 4 km/h + 2 km/h = 6 km/h.

Correct Answer: C — 6 km/h

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Q. A physical quantity is measured as 50.0 units with an uncertainty of ±1.0 units. If this quantity is multiplied by 3, what is the new uncertainty?

A. 3.0 units
B. 1.0 units
C. 2.0 units
D. 4.0 units

Solution

New uncertainty = 3 * (uncertainty) = 3 * 1.0 = 3.0 units.

Correct Answer: A — 3.0 units

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Q. A plane flies 300 km north and then 400 km east. What is the angle of the resultant displacement with respect to the north?

A. 36.87 degrees
B. 45 degrees
C. 53.13 degrees
D. 60 degrees

Solution

Angle = tan^(-1)(400/300) = 53.13 degrees.

Correct Answer: C — 53.13 degrees

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Q. A plane flies at a speed of 200 m/s at an angle of 30 degrees to the horizontal. What is the vertical component of its velocity?

A. 100 m/s
B. 150 m/s
C. 200 m/s
D. 250 m/s

Solution

Vertical component (v_y) = v * sin(θ) = 200 * (√3/2) ≈ 173.2 m/s.

Correct Answer: A — 100 m/s

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Q. A plane is flying at 200 m/s in still air. If there is a headwind of 50 m/s, what is the speed of the plane relative to the ground?

A. 150 m/s
B. 200 m/s
C. 250 m/s
D. 300 m/s

Solution

Speed relative to ground = Speed of plane - Speed of wind = 200 m/s - 50 m/s = 150 m/s.

Correct Answer: A — 150 m/s

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Q. A planet orbits a star in an elliptical path. What remains constant throughout its orbit?

A. Angular momentum
B. Kinetic energy
C. Potential energy
D. Total energy

Solution

Angular momentum is conserved in the absence of external torques, even in elliptical orbits.

Correct Answer: A — Angular momentum

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Q. A planet orbits the sun in a circular path. If the radius of the orbit is doubled, what happens to the angular momentum of the planet if its speed remains constant?

A. Doubles
B. Halves
C. Remains the same
D. Quadruples

Solution

Angular momentum L = mvr, so if the radius is doubled and speed remains constant, angular momentum doubles.

Correct Answer: A — Doubles

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Q. A planet orbits the sun in a circular path. If the radius of the orbit is halved, what happens to the angular momentum of the planet?

A. It doubles
B. It halves
C. It remains the same
D. It becomes zero

Solution

Angular momentum L = mvr; if the radius is halved and speed remains constant, angular momentum halves.

Correct Answer: B — It halves

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Q. A planet orbits the sun in an elliptical path. What remains constant for the planet as it moves in its orbit?

A. Kinetic energy
B. Potential energy
C. Angular momentum
D. Total energy

Solution

Angular momentum remains constant for a planet in orbit due to the conservation of angular momentum.

Correct Answer: C — Angular momentum

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Q. A planet orbits the sun in an elliptical path. Which of the following statements is true regarding its angular momentum?

A. It is constant.
B. It varies with distance from the sun.
C. It is zero at perihelion.
D. It is maximum at aphelion.

Solution

The angular momentum of a planet about the sun is conserved as there is no external torque acting on it.

Correct Answer: A — It is constant.

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