Test: Motion in a Plane (May 21) - JEE MCQ

A ball is projected from the ground with a speed 15 ms^-1 at an angle θ with horizontal so that its range and maximum height are equal, then tan θ will be equal to

A ball is projected vertically upward with an initial velocity of 50 ms^-1 at t = 0 s. At t = 2 s, another ball is projected vertically upward with same velocity. At t = _______ s, second ball will meet the first ball (g = 10 ms^-2). (in integers)

A swimmer can swim with velocity 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is __________ (in degrees).
(Round off to the nearest integer)

A person is swimming with a speed of 10 m/s at an angle of 120° with the flow and reaches a point directly opposite on the other side of the river. The speed of the flow is 'x' m/s. The value of 'x' to the nearest integer is ______.

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30° with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle θ with the line AB should be _____ °, so that the swimmer reaches point B. (in integers)

At time t = 0, a particle starts travelling from a height 7 cm in a plane keeping z coordinate constant. At any instant of time, its position along the  and  directions is defined as 3t and 5t³, respectively. At t = 1 s, acceleration of the particle will be

The resultant of these force  and  is approximately ___________ N.
[Take  = 1.7,  = 1.4 Given  and  unit vector along x, y axis]

Two vectors  and  have equal magnitudes. If magnitude of  is equal to two times the magnitude of , then the angle between  and  will be:

A body of mass 2 kg moves under a force of N. It starts from rest and was at the origin initially. After 4s, its new coordinates are (8, b, 20). The value of b is ________. (Round off to the nearest integer)

Statement I: Two forces  and  where , when act at an angle  to each other, the magnitude of their resultant is , when they act at an angle , the magnitude of their resultant becomes  . This is possible only when .

Statement II: In the situation given above.
 = 60° and  = 90°

In the light of the above statements, choose the most appropriate answer from the options given below

A particle of mass m is projected with a speed u from the ground at an angle θ = π / 3 w.r.t. horizontal axis (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity u. The horizontal distance covered by the combined mass before reaching the ground is:

From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s. A third ball released, from the rest from the same location, will reach the ground in ____ s.(In Integers)