1)  A taxi drives 300.0 m south and then turns and drives 180.0 m east. What is the total displacement of the taxi?

2. What is the total displacement of two trips, one of 10.0 km [N] and the other of 24 km [E]?

3. A horse runs 15 m [N 23° E] and then 32 m [S 35° E]. What is the total displacement of the horse?

4. A car travels 28 m [E 35° S] and then turns and travels 45 m [S]. The whole motion takes 6.9s.

(a) What is the car's average velocity?

(b) What is the car's average speed?

5. An aircraft experiences a displacement of 100.0 km [N 30° E] due to its engines. The aircraft also experiences a displacement of 50.0 km [W] due to the wind.

(a) What is the total displacement of the aircraft?

(b) If it takes 10.0 min for the motion to occur, what is the average velocity, in kilometres per hour, of the aircraft during this motion?

 

Answer:

1) (Figure is attached in explanation)

y₁= 300m south , x₁=180m east

Displacement=?x2+y2?? =?1802+3002?? =349.85 m

Total Displacement =349.85 m

2)(Figure is attached in explanation)

y₁= 10 km north , x₁=24km east

Displacement=?x2+y2?? =?242+102?? =240.20 m

Total Displacement =240.20 m

3) (Figure is attached in explanation).This problem is not easy as the first two problems, since the directions are making angles with axes we have to take the x and y components and thus find the effective displacements.

First horse runs 15 m N 23^o E , then runs 32 m S 35^o E

Splitting the into components

x₁=15*sin 23 =5.86 m y₁=15*cos 23=-13.80 m(direction is considered-upward negative)

x₂=32*sin 35=18.35 m y₂=32*cos 35=26.212 m

From components , X_effective=x₁+x₂=5.86+18.35=24.21

Y_effective=Y₁+Y₂=26.212-13.80(considering directions)=12.41

Displacement=?Xeffective2+Yeffective2?? =?24.212+12.412??? =27.20 m

Total displacement = 27.20 m

4)

a)(Figure is attached in explanation). As last question here also we have to split the displacements into components for finding effective total displacement.

 28 m [E 35° S] and then turns and travels 45 m [S]

x₁=28*cos35=22.93 m y₁=28*sin35=16.06 m

x₂=0 m y₂=45 m

From components , X_effective=x₁+x₂=22.93+0=22.93 m

Y_effective=Y₁+Y₂=16.06+45=61.06 m

Displacement=?Xeffective2+Yeffective2?? =?22.932+61.062?? =65.22 m

Total displacement = 65.22 m

b) Av. speed=Total distance/Total time = (28+45)/6.9 =10.58 m/s

5)

a)(Figure is attached in explanation). As last question here also we have to split the displacements into components for finding effective total displacement in this question.

100.0 km [N 30° E] due to its engines, 50.0 km [W] due to the wind.

x₁=100*sin 30=50 km y₁=100*cos30=86.60 km

x₂=-50 km(Direction-to left side negative) y₂=0 km

From components , X_effective=x₁+x₂=50-50=0 km

Y_effective=Y₁+Y₂=86.60+0=86.60 km

Displacement=?Xeffective2+Yeffective2?? =?86.602?? =86.60 km

Total displacement = 86.60 km

b)Average velocity(in km/hr)=Total displacement / Total time in hours =86.60/(10/60) =519.6 km/ hr

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