Motion in a Plane

The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the bank is cm. (Take g = 10 m/s2)

The position vector of a moving body at any instant of time is given as r= (5t2 i-5t j ) m. The magnitude and direction of velocity at t=2 s is,

1. 5 17 m/s, making an angle of -14 with -ve Y axis
2. 5 15 m/s, making an angle of -14 with +ve X axis
3. 5 17 m/s, making an angle of -14 with +ve X axis
4. 5 15 m/s, making an angle of -14 with -ve Y axis

Two particles are located at equal distance from origin. The position vectors of those are represented by A=2 i+3n j+2 k and B=2 i-2 j+4p k, respectively. If both the vectors are at right angle to each other, the value of n-1 is .

A ball having kinetic energy KE, is projected at an angle of 60 from the horizontal. What will be the kinetic energy of ball at the highest point of its flight?

1. (KE)2
2. (KE)8
3. (KE)4
4. (KE)16

A particle is projected at an angle of 30 from horizontal at a speed of 60 m/s. The height traversed by the particle in the first second is h0 and height traversed in the last second, before it reaches the maximum height, is h1. The ratio h0:h1 is . [Take, g=10 m/s2 ]

If a and b make an angle -1 ( 59 ) with each other, then | a + b| = 2| a - b| for | a| = n| b|. The integer value of n is .

The resultant of two vectors A and B is perpendicular to A and its magnitude is half that of B. The angle between vectors A and B is .

A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the tip of minute hand. The value of x in meter is nearly (Take = 3.14) :

1. 118.9
2. 140.5
3. 139.4
4. 220.0

Three vectors OP, OQ and OR each of magnitude A are acting as shown in figure. The resultant of the three vectors is A x. The value of x is . [figure]

The angle of projection for a projectile to have same horizontal range and maximum height is :

1. -1 ( 12 )
2. -1(2)
3. -1 ( 14 )
4. -1(4)