Vector and Motion in Plane

1. A man can swim with a speed of 4km/h in still water, how long does he take a cross a river 1km wide if the river flows steadily at 3km/h and he makes his stroke normal to the river current ? How far down the river does he go when he reaches the other bank

• Ans 0.25h, 0.75km
• Ans 0.25h, 0.35km
• Ans 0.5h, 0.75km
• Ans 0.25h, 1km

2. A lady walking due east on a road with velocity of 10m/s encounters rain falling vertically with a velocity of 30m/s , at what angle she should hold her umbrella to protect herself from the rain

• tan θ=1/2
• tan θ=1/3
• tan θ=1/6
• tan θ=1/7

3. Two forces whose magnitudes are in the ratio of 3:5 give a resultant 35N , if the angle of inclination is 600 , Find the magnitude of each force.

• 15N , 55N
• 15N , 35N
• 25N , 35N
• 15N , 25N

4.Find the angle between A =i ̂+2J ̂-K ̂ and B = -i ̂+J ̂-2K ̂

• 10 degree
• 45 degree
• 60 degree
• 90 degree

10 Find the area of Triangle whose base is given by A =i ̂+J ̂+K ̂ and one of other side is B= 2J ̂ +K ̂

• 1.335 sq. unit
• 1.225 sq . unit
• 1.5sq. unit
• none of these

5. Find the value of n for which A =2i ̂+4J ̂-nK ̂ is perpendicular to B==3i ̂-(4J) ̂-2K ̂

• 2
• 3
• 4
• 5

6. What is the angle of projection of an oblique projectile if its range is √3 u 2/2g

• 20 degree
• 30 degree
• 45 degree
• 60 degree

7. Prove that the maximum horizontal range is four times the maximum height attained by a projectile which is fired along the required oblique direction

• Rmax =4H
• Rmax =5H
• Rmax =6H
• none of these

8. A ball of mass m is thrown vertically up, another ball of mass 2m is thrown at an angle θ with the vertical both of them stay in air for same period of time, what is the ratio of height attained by the two balls Ans 1:1

• 1:1
• 1:2
• 1:3
• 1:4

9. Two projectile are fired with the same velocity, if one is projected at an angle 30 degree and other at 60 degree to the horizontal , then find the ratio of horizontal range ?

• 1:2
• 1:3
• 1:8
• 1:1