Motion in plane practice · Medium

A projectile has initially the same horizontal velocity as it would acquire if it had moved from rest with uniform acceleration of $3 \mathrm{~m} \mathrm{s}^{-2}$ for 0.5 minutes. If the maximum height reached by it is $80 \mathrm{~m}$, then the angle of projection is
(Take $g=10 \mathrm{~m} \mathrm{s}^{-2}$ )

Two projectiles A and B are thrown with the same speed such that A makes angle $\mathrm{q}$ with the horizontal and B makes angle $q$ with the vertical, then

Consider the following statements about three vectors $\overrightarrow{{a}}, \overrightarrow{{b}}$ and $\overrightarrow{{c}}$ that have non-zero magnitudes. It follows $\overrightarrow{{b}}=\overrightarrow{{c}}$

(i) if $\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}$

(ii) if $\vec{a} \times \vec{b}=\vec{a} \times \vec{c} \quad \vec{b}$ must be perpendicular to $\overrightarrow{\mathrm{c}}$

Statement-I: Two bodies thrown with same speed from the same point at the same instants but at different angles never collide in air.
Statement-II: $x$ and $y$ co-ordinates of the two projectiles always differ

Statement-I: Minimum number of non-equal vectors in a plane required to give zero resultant is three.
Statement-II: If $\vec{a}+\vec{b}+\vec{c}=0$, then they must lie in one plane

Assertion: Two projectiles of masses $m$ and $4m$ when projected with same initial velocity vector have different ranges.
Reason: The horizontal range of a projectile depends on mass of the body.

The component of a vector r along X-axis will
have a maximum value, if :

A body constrained to move along the $z$-axis of a co-ordinate system is subjected to a constant force $\vec{F}$ given by $\vec{F}=-\hat{i}+2 \hat{j}+3 \hat{k}$ newton where $\hat{i}, \hat{j}$ and $\hat{k}$ represent unit vectors along $x,y$ and $z$-axis of the system respectively. Calculate the work done by the force in displacing the body through a distance of $4 \mathrm{~m}$ along the $z$-axis.

A particle moves in $X Y$-plane from positions $(2 \mathrm{~m}, 4 \mathrm{~m})$ to $(6 \mathrm{~m}, 8 \mathrm{~m})$ is $2 \mathrm{~s}$. Magnitude and direction of average velocity is

Can scalar product be ever negative?

Which of the following statement is correct?

Assertion: A coin is allowed to fall in a train moving with constant velocity. Its trajectory is a straight line as seen by an observer attached to the train.
Reason: An observer on ground will see the path of coin as a parabola.

Two vectors are perpendicular, if

Assertion: Generally the path of a projectile from the earth is parabolic but it is elliptical for projectiles going to a very great height.

Reason: Up to ordinary height the projectile moves under a uniform gravitational force, but for great heights, projectile moves under a variable force.

The horizontal and vertical displacements $x$ and $y$ of projectile at a given time $t$ are given by $x = 12\,t\,m$ and $y = 5t - 5{t^2}\,m$. The range of the projectile in metres is

Which of the following is not true? If $\vec{A}=3 \hat{i}+4 \hat{j}$ and $\vec{B}=6 \hat{i}+8 \hat{j}$ where $A$ and $B$ are the magnitudes of $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$

The resultant of two forces 3P and 2P is R. If the first force is doubled them the resultant is also doubled. The angle between the two forces is

A force is inclined at $50^{\circ}$ to the horizontal. If its rectangular component in the horizontal direction be $50 \mathrm{~N}$, find the magnitude of the force and its vertical component.

Assertion: Adding a scalar to a vector of the same dimensions is a meaningful algebraic operation.
Reason : Displacement can be added to distance.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: When a body is projected at an angle $45^{\circ},$ it's range is maximum.

Reason R: For maximum range, the value of $\sin 2 \theta$ should be equal to one.

In the light of the above statements, choose the correct answer from the options given below:

The resultant of the tow vectors having magnitude 2 and 3 is 1. What is their cross product.

It is found that $\left| {A + B} \right| = \left| A \right|,$ this necessarily implies

One fielder throws a ball and in 4 secs it reaches to another player. So, the maximum height reached by the ball above the point of projection would be about

A projectile is fired at an angle of 30° to the horizontal such that the vertical component of its initial velocity is $80\mathrm{\;m}{\mathrm{s}^{ - 1}}$. Its time of flight is T. Its velocity at $t = \frac{T}{4}$ has a magnitude of nearly

The angle between vector $\overrightarrow{Q}$ and the resultant of $(2 \overrightarrow{Q}+2 \overrightarrow{{P}})$ and $(2 \overrightarrow{{Q}}-2 \overrightarrow{{P}})$ is:

Two forces of $5 \mathrm{~N}$ and $7 \mathrm{~N}$ act on a particle with an angle of $60^\circ$ between them. Find the resultant force.

The torque force $\bar F = 2i - 3j + 4k$ newtons acting at the point $\bar r = 3i + 2j + 3k$ meters about the origin is

Choose the wrong statement.

An ant starts from the origin and crawls $10 \mathrm{~cm}$ along the $x$ - axis and then $20 \mathrm{~cm}$ along the $y-$ axis. The dot product of the ant's displacement vector with the position vector of a point that makes $45^{\circ}$ with the $x$ - axis and has a magnitude of $\sqrt{2} \mathrm{~cm}$ is

Minimum number of vectors of unequal magnitude whose vector sum can equal to zero is