Q28 of 37 Page 23

If |A|= 2 and |B| = 4, then match the relations in column I with the angle θ between A and B in column II

Given:


|A| = 2, |B| = 4.


(a)


So,


So, θ = 0°


Option (a) matches with (iv)


(b)


So,


So, θ = 90°


Option (b) matches with (iii)


(c)


So,


So, θ = 30°


Option (c) matches with (i)


(d)


So,


So, θ = 45°


Option (d) matches with (ii)


More from this chapter

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26

Given below in column I are the relations between vectors a, b and c and in column II are the orientations of a, b and c in the XY plane. Match the relation in column I to correct orientations in column II.

Column I


(a) a + b = c


(b) a – c = b


(c) b – a = c


(d) a + b + c = 0


Column II






 27

If |A| = 2 and |B| = 4, then match the relations in column I with the angle θ between A B and in column II.

 29

A hill is 500 m high. Supplies are to be sent across the hill using a canon that can hurl packets at a speed of 125 m/s over the hill. The canon is located at a distance of 800m from the foot of hill and can be moved on the ground at a speed of 2 m/s; so that its distance from the hill can be adjusted. What is the shortest time in which a packet can reach on the ground across the hill? Take g =10 m/s2.

 30

A gun can fire shells with maximum speed vo and the maximum horizontal range that can be achieved is R = .


If a target farther away by distance ∆x (beyond R) has to be hit with the same gun (Fig 4.5), show that it could be achieved by raising the gun to a height at least


h = ∆x


(Hint: This problem can be approached in two different ways:


(i) Refer to the diagram: target T is at horizontal distance x = R + ∆x and below point of projection y = – h.


(ii) From point P in the diagram: Projection at speed vo at an angle θ below horizontal with height h and horizontal range ∆x.)