Motion in plane practice · Medium

Which of the following statement(s) is/are correct?

Consider the following statements and select the correct statements from the following.
I. Addition and subtraction of scalars make sense only for quantities with same units
II. Multiplication and division of scalars with different units is possible
III. Addition, subtraction, multiplication and division of scalars with same unit is possible

Pressure is a scalar quantity because

An aeroplane moving horizontally at a speed of $200\mathrm{\;m}{\mathrm{s}^{ - 1}}$ and at a height of $8 \times {10^3}\mathrm{m}$ is to drop a bomb on a target. At what horizontal distance from the target should the bomb be released? (Take $\mathrm{g} = 10\mathrm{\;m}{\mathrm{s}^{ - 2}}$)

A body is under the action of two mutually perpendicular forces of 3 N and 4 N. The resultant force acting on the body is

A body when projected vertically up, covers a total distance $s$, during its time of flight. If we neglect gravity then how much distance the particle will travel during the same time. Will it fall back?

The angle between two vectors $A$ and $B$ is $\theta$. Vector $R$ is the resultant of the two vectors. If $R$ makes an $\frac{\theta}{2}$ with $A$, then

The trajectory of a projectile in a vertical plane is $y = \alpha x - \beta {x^2}$, where $\alpha$ and $\beta$ are constants $x$ and $y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained $H$ are respectively given by

The position of particle is given by $\vec{r}=2 t^2 \hat{i}+3 t \hat{j}+4 \hat{k}$ where $t$ is in second and the coefficients have proper units for $\vec{r}$ to be in metre. The $\vec{a}(t)$ of the particle at $t=1 \mathrm{~sec}$ is:

Select the incorrect statement(s) from the following.
I. In projectile motion, the range depends on the mass. It is greater for heavier object
II. In projectile motion, the range is independent of the angle of projection.

A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?

Statement-I: Two particles of different mass, projected with same velocity at same angles. The maximum height attained by both the particle will be same.
Statement-II: The maximum height of projectile is independent of particle mass.

If ${A}=\hat{{i}}+2 \hat{{k}}$ and ${B}=\hat{{j}}-\hat{{k}}$, then, ${A} \times {B}$ is equal to

Statement-I: The value of $\hat{\mathrm{i}}(\hat{\mathrm{j}} \times \hat{\mathrm{k}})+\hat{\mathrm{j}}(\hat{\mathrm{k}} \times \hat{\mathrm{i}})+\hat{\mathrm{k}} \cdot(\hat{\mathrm{i}} \times \hat{\mathrm{j}})$ is equal to 3
Statement-II: If $\hat{a}, \hat{b}, \hat{c}$ are mutually perpendicular unit vectors, then $[\hat{a}, \hat{b}, \hat{c}]=1$

Assertion: A physical quantity can be a vector, if magnitude as well as direction is associated with it.
Reason: A physical quantity can be a scalar quantity, if it is associated with magnitude only.

Assertion: Two vectors $\vec{A}$ and $\vec{B}$ are said to be equal if they have the same magnitude and direction.
Reason: Addition and subtraction of scalars is possible only for quantities having same units.

The angle between the two vectors $- 2\hat i + 3\hat j - \hat k$ and $\hat i + 2\hat j + 4\hat k$ is

If ${A} \cdot {B}=0$ and ${A} \times {B}=1$, then ${A}$ and ${B}$ are

The area of triangle whose adjacent sides are represented by the vectors $(4i + 3j + 4k)$ and $5\bar i$ in sq. unit is

Three vectors $A={a} \hat{{i}}+\hat{{j}}+\hat{{k}} ; {B}=\hat{{i}}+{b} \hat{{j}}+\hat{{k}}$ and $\mathrm{C}=\hat{{i}}+\hat{{j}}+\mathrm{c} \hat{{k}}$ are mutually perpendicular $(\hat{{i}}, \hat{{j}}$ and $\hat{{k}}$ are unit vectors along $X, Y$ and $Z$ - axis respectively). The respective values of $a, b$ and $c$ are

The range of a projectile is $R$ when the angle of projection is $40^{\circ}.$ For the same speed of projection and same range, the other possible angle of projection is:

When two vectors $\vec{A}$ and $\vec{B}$ of magnitude $a$ and $b$ are added, the magnitude of the resultant vector is always

Vector $\mathbf{P}=6 \hat{\mathbf{i}}+4 \sqrt{2} \hat{\mathbf{j}}+4 \sqrt{2} \hat{\mathbf{k}}$ makes an angle with $Z$-axis which is equal to

The resultant of two forces $P$ and $Q$ is of magnitude $P$. If $P$ be doubled, the resultant will be inclined to $Q$ at an angle.

Four projectiles are fixed with the same velocities at angles $25^{\circ}, {4 0}^{\circ}, 55^{\circ}$ and $70^{\circ}$ with the horizontal. The range of projectile will be largest for the one projected at angle

From a point on the ground, a particle is projected slantwise with some initial velocity making an acute angle with the horizontal. During its flight, the dot product of its velocity and acceleration vectors

Statement-I: The scalar product of a force $\vec{F}$ and displacement $\vec{r}$ is equal to the work done.
Statement-II: Work done is not a scalar.

Surface area is

Two vectors are given by $\vec{A}=(3 \hat{i}+\hat{j}+3 \hat{k})$ and $\vec{B}=(3 \hat{ i }+5 \hat{ j }-2 \hat{ k })$. Find the third vector $\vec{ C }$ if $\vec{ A }+3 \vec{ B }-\vec{ C }=0$

An aeroplane is flying at a height of 1960 m in horizontal direction with a velocity of 360 km / hr. When it is vertically above the point. A on the ground, it drops a bomb. The bomb strikes a point B on the ground, then the time taken by the bomb to reach the ground is-