PSC # 2 VECTORS and SCALARS NU-CPS Physics 2014-15

1.Complete the sentences

The resultant of vector and vector is vector …

The resultant of vector and vector is vector …

2.A displacement vector has a magnitude of 12.0 km in the direction 40.0° east of north.

(a) What is the north component of the vector?

(b) What is the east component?

3.Find the components of the vector of length 10.0 m in three different frames a) (x,y); b) (x’,y’) and c) (x’’,y’’).

4.Find the angle between vectors = 2 – and = + 2

5.Given that = 6 – 2 and = -4 – 3 + 2 , find vector such that the following is true: 3 - 2 = 4 .

6.A river flows due east at 2.00 m/s. A boat crosses the river from the south shore to the north by maintaining a constant velocity of 10.0 m/s due north relative to the water.

(a) What is the velocity of the boat relative to the shore?

(b) If the river is 300m wide, how far downstream has the boat moved by the time it reaches the north shore?

7.By clearly showing all steps prove that for any two vectors =x₁ + y₁ + z₁ and =x₂ + y₂ + z₂ , the scalar product is given by · = x₁ x₂ + y₁ y₂ + z₁ z_{2 .}

8.By clearly showing all steps prove that · =|a||b|cosθ.

9.A plane is travelling eastward at a speed of 500 km/hr. At the same time, a 90.0 km/hr wind is blowing southward. What are the direction and speed of the plane relative to the ground?

10.A bus is traveling along a straight highway at a constant speed 55.0 km/hr. A person sitting at rest on the bus fires a dart gun.The dart moves straight backward with a velocity of 45.0 km/hr. Find the velocity of the dart, relative to the road, as it leaves the gun.

PSC 2 Numerical Answers:

1. Vector , vector .

2. a) north component = 9.19 km, b) east component = 7.71 km.

3. a) (10.0,0); b) (-10.0,0); c) (-5.0, -8.66).

4. 90 degrees.

5. = 17 + 3 + (-4) .

6. a) _bs= 10.2 m/s, at angle of 78.7⁰ N of E, or 11.3⁰ E of N,

or bearing 11.3⁰

b) distance downstream = 60.0 m.

7. Proof has no numerical answer.

Hint: (x₁ ) · (x₂ ) = x₁x₂; and (x₁ ) · (y₁ )= 0 since θ between = 90^o.

8. Use result of 7) and recall trig identity cos (α - β) = cos α cos β + sin α sin β .

9. _pe= 508 km/hr, at angle of 10.2⁰ S of E, or 79.8⁰ E of S,

or bearing 100.2⁰.

10. _dr= 10.0 km/hr, in the same direction of the bus relative to the road.

Date: 2015-01-29; view: 4406