Kinematics

A block 'A' takes 2 s to slide down a frictionless incline of 30° and length '$l$', kept inside a lift going up with uniform velocity '$v$'. If the incline is changed to 45°, the time taken by the block, to slide down the incline, will be approximately :

The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at $(4+x)$ cm inside the block. The value of $x$ is :

Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top Point B at a height 10 m. After reaching the Point B the block slides down on inclined plane BC. Time it takes to reach to the point C from point A is $t\left(\sqrt2+1\right)$ s. The value of t is ______.

(use g = 10 m/s$^2$)

A NCC parade is going at a uniform speed of 9 km/h under a mango tree on which a monkey is sitting at a height of 19.6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is :

(Given g = 9.8 m/s$^2$)

If the projection of $2\hat i+4\hat j-2\hat k$ on $\hat i+2\hat j+\alpha\hat k$ is zero. Then, the value of $\alpha$ will be ______.

At time t = 0 a particle starts travelling from a height $7\hat z$ cm in a plane keeping z coordinate constant. At any instant of time it's position along the $\hat x$ and $\hat y$ directions are defined as 3t and 5t$^3$ respectively. At t = 1 s acceleration of the particle will be

A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to 40 J within 1 s, the minimum length of the pool, the bullet has to travel so that it completely comes to rest is

A uniform electric field E = (8m/e) V/m is created between two parallel plates of length 1 m as shown in figure, (where m = mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of 2 m/s. The angle of the deviation (θ) of the path of the electron as it comes out of the field will be ______.

A ball is thrown vertically upwards with a velocity of 19.6 ms$^{-1}$ from the top of a tower. The ball strikes the ground after 6 s. The height from the ground up to which the ball can rise will be $\left(\dfrac k5\right)$ m. The value of k is ______ (use g = 9.8 m/s$^2$)

A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height $\dfrac h3$ while going up and coming down respectively.

If $t=\sqrt x+4$, then $\left(\dfrac{dx}{dt}\right)_{t=4}$ is :

A ball is projected with kinetic energy E, at an angle of 60° to the horizontal. The kinetic energy of this ball at the highest point of its flight will become :

An object is projected in the air with initial velocity u at an angle θ. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be _______ degree.

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is

A ball is released from a height h. If $t_1$ and $t_2$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_1$ and $t_2$.

Two trucks A and B are approaching each other on a straight path with the velocities of 16 m/s and 20 m/s respectively. When they are 200 m apart their drivers see each other and applies the breaks simultaneously. If the truck A decelerates with 2 m/s$^2$ and truck B decelerates with 4 m/s$^2$, what is the distance between them when they finally stop?

Two projectiles are thrown towards each other at 15° and 45° angles respectively with the horizontal at the same speed. The difference between the horizontal distances traveled by the two projectiles is 80 m. The initial speed of the projectiles is _______ m s$^{-1}$ [Given g = 10 m s$^{-2}$]

The value of $t$ is ____.

The value of $x$ is ____.

A particle of mass $M = 0.2$ kg is initially at rest in the $xy$-plane at a point $(x = -l, y = -h)$, where $l = 10$ m and $h = 1$ m. The particle is accelerated at time $t = 0$ with a constant acceleration $a = 10\ \text{m/s}^2$ along the positive $x$-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by $\vec L$ and $\vec\tau$, respectively. $\hat i$, $\hat j$ and $\hat k$ are unit vectors along the positive $x$, $y$ and $z$-directions, respectively. If $\hat k = \hat i \times \hat j$ then which of the following statement(s) is(are) correct?