Motion in A Pla...

The vector projection of a \(3\hat i + 4 \hat k\) vector on y-axis is

A force of 5 N acts on a particle along a direction making an angle of 60° with vertical. Its vertical component be

The direction of cosines of the \(\vec A=2\hat i+4\hat j-5\hat k\) are

How much minimum number of coplanar vectors having different magnitudes can be added to give zero resultant?

A hall has the dimensions (10m) × (12m) × (14m). A fly starting at one corner ends up at a diametrically opposite corner. What is the magnitude of its displacement?

The unit vector along \(\hat i + \hat j\) is

Five equal forces of 10 N each are applied at one point and all are lying in one plane. If the angles between them are equal, the resultant force will be

If a unit vector is represented by \(0.5 \hat i + 0.8 \hat j + c \hat k\), then the value of c is

A boy walks uniformally along the sides of a rectangular park of size 400 m× 300 m, starting from one corner to the other corner diagonally opposite. Which of the following statement is incorrect?

A stone is projected horizontally with a 5 m/s from the top of a plane inclined at an angle 45° with the horizontal. How far from the point of projection will the particle strike the plane?

Two balls are projected at an angle θ and (90°−θ) to the horizontal with the same speed. The ratio of their maximum vertical heights is:

The vector that must be added to the vector \(\hat i - 3 \hat j + 2 \hat k\) and \(3\hat i - 6 \hat j + 7 \hat k\) so that the resultant vector is a unit vector along the y-axis, is 

A particle crossing the origin of co-ordinates at time t = 0, moves in the xy-plane with a constant acceleration a in the y-direction. If its equation of motion is y = \(bx^2\) (b is a constant), its velocity component in the x-direction is

A plane flying horizontally at a height of 1500 m with a velocity of 200 \(ms^{-1}\) passes directly overhead on antiaircraft gun. Then the angle with the horizontal at which the gun should be fired from the shell with a muzzle velocity of 400 \(ms^{-1}\) to hit the plane, is

The equation of trajectory of projectile is given where x and y are in meter. The maximum range of the projectile is y = \(\frac{x}{\sqrt 3} - \frac{gx^2}{20}\)

Assertion: In projectile motion, the angle between the instantaneous velocity and acceleration at the highest point is 180°.

Reason: At the highest point, velocity of projectile will be in horizontal direction only.

(A) If both assertion and reason are true and the reason is the correct explanation of the assertion. 

(B) If both assertion and reason are true but reason is not the correct explanation of the assertion. 

(C) If assertion is true but reason is false.

(D) If the assertion and reason both are false.

(E) If assertion is false but reason is true.

If a particle moves in a circle describing equal angles in equal times, its velocity vector

Assertion: The trajectory of projectile is quadratic in y and linear in x.

Reason: y component of trajectory is independent of x-component.

(A) If both assertion and reason are true and the reason is the correct explanation of the assertion.           

(B) If both assertion and reason are true but reason is not the correct explanation of the assertion.           

(C) If assertion is true but reason is false.           

(D)  If the assertion and reason both are false.