Real-Life Applications of Vector Addition, Vector Subtraction, Sine Law & Cosine Law - Worksheet

 

Worksheet: Real-Life Applications of Vector Addition, Vector Subtraction, Sine Law & Cosine Law

JEE Main • NEET • CBSE Class 11 Physics

Total Questions: 20 MCQs
Topics Covered:

• Vector Addition
• Vector Subtraction
• Parallelogram Law
• Triangle Law
• Sine Law
• Cosine Law
• Boat/Man Swimming Across a River
• Rain and Wind Problems
• Relative Velocity
• Ship and Flag Problems
• Airplane Crosswind Problems

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Questions

1.

A man swims across a river flowing east with speed 4 m/s. He swims due north at 3 m/s relative to water. His resultant speed with respect to the ground is

A) 1 m/s

B) 5 m/s

C) 7 m/s

D) 12 m/s

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2.

A river is 240 m wide. The swimmer's speed perpendicular to the river bank is 6 m/s. Time taken to cross the river is

A) 20 s

B) 30 s

C) 40 s

D) 60 s

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3.

A boat moves north at 8 km/h in still water. River current flows east at 6 km/h. The direction of resultant velocity with respect to north is

A) 30°

B) 37°

C) 45°

D) 53°

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4.

Rain falls vertically downward at 12 m/s. Wind blows horizontally at 5 m/s. The angle made by rain with the vertical is

A) 18°

B) 23°

C) 45°

D) 67°

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5.

A cyclist rides east at 10 m/s. Rain falls vertically downward at 10 m/s. The apparent direction of rain with respect to the cyclist makes an angle with the vertical equal to

A) 30°

B) 45°

C) 60°

D) 90°

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6.

A person standing still observes rain falling vertically. A cyclist moving east observes the rain slanting towards

A) East

B) West

C) North

D) South

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7.

A ship sails north at 20 km/h while the wind blows east at 15 km/h. The flag on the ship appears to flutter towards

A) North-East

B) South-West

C) North-West

D) South-East

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8.

A helicopter flies due north at 120 km/h while wind blows east at 50 km/h. The actual speed of helicopter relative to the ground is

A) 130 km/h

B) 150 km/h

C) 170 km/h

D) 110 km/h

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9.

Two ropes pull a box with forces 40 N and 30 N making an angle of 90°. The resultant force is

A) 10 N

B) 50 N

C) 70 N

D) 120 N

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10.

Two forces of 10 N and 10 N act at an angle of 120°. Their resultant is

A) 10 N

B) 20 N

C) 5 N

D) 15 N

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Cosine Law Applications

11.

Two displacement vectors of 6 km and 8 km make an angle of 60°. The resultant displacement is

A) 10 km

B) 12 km

C) 7 km

D) 14 km

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12.

A rescue team walks 12 km east and then 5 km north. The shortest distance from the starting point is

A) 13 km

B) 17 km

C) 7 km

D) 10 km

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13.

A person walks 10 km north and then 10 km east. The angle between the resultant displacement and east direction is

A) 30°

B) 45°

C) 60°

D) 90°

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14.

Two vectors have magnitudes 15 N and 20 N with an angle of 180°. Resultant magnitude is

A) 5 N

B) 35 N

C) 25 N

D) 15 N

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15.

A pilot flies 300 km north while wind pushes the airplane 400 km east. The displacement from the starting point is

A) 500 km

B) 600 km

C) 700 km

D) 350 km

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Sine Law Applications

16.

A surveyor measures two sides of a triangular field as 80 m and 60 m with included angle 90°. The third side is

A) 100 m

B) 120 m

C) 140 m

D) 70 m

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17.

A rescue drone travels 15 km north-east making 45° with east. Its eastward component is

A) 15 km

B) 10.6 km

C) 7.5 km

D) 12 km

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18.

A man walks 6 km east and then 8 km north. The direction of resultant with east is

A) 37°

B) 45°

C) 53°

D) 60°

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19.

An airplane experiences two velocity vectors of 300 km/h and 400 km/h acting at right angles. The resultant velocity is

A) 500 km/h

B) 600 km/h

C) 700 km/h

D) 350 km/h

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20.

Two equal forces of 50 N act at an angle of 60°. Their resultant is

A) 50 N

B) 100 N

C) $50\sqrt{3}$ N

D) $25\sqrt{3}$ N

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Answer Key

Q.No	Answer	Q.No	Answer
1	B	11	B
2	C	12	A
3	B	13	B
4	B	14	A
5	B	15	A
6	B	16	A
7	B	17	B
8	A	18	C
9	B	19	A
10	A	20	C

This worksheet is designed in the style of JEE Main, NEET, and CBSE Class 11 examinations, with a strong emphasis on real-life vector applications, relative velocity, river crossing, rain and wind, ship and flag motion, and the use of the sine rule and cosine rule in solving practical physics problems.