A projectile is given an initial velocity of $(\hat i + 2\hat j)\ ms^{-1}$, where $\hat i$ is along the ground and $\hat j$ is along the vertical. If $g = 10\ m/s^2$ , the equation of its trajectory is

The initial velocity of a projectile is $\vec u = (4\hat i + 3\hat j)\,m/s$ it is moving with uniform acceleration $\vec a = (0.4\hat i + 0.3\hat j)\, m/s^2$ The magnitude of its velocity after $10\,s$ is.........$m/s$

What can be the angle between velocity and acceleration for the motion in two or three dimension ?

Read each statement below carefully and state, with reasons and examples, if it is true or false :

A scalar quantity is one that

$(a)$ is conserved in a process

$(b)$ can never take negative values

$(c)$ must be dimensionless

$(d)$ does not vary from one point to another in space

$(e)$ has the same value for observers with different orientations of axes.

The trajectory of projectile, projected from the ground is given by $y=x-\frac{x^2}{20}$. Where $x$ and $y$ are measured in meter. The maximum height attained by the projectile will be $...........\,m$

If a particle takes $t$ second less and acquires a velocity of $v \ ms^{^{-1}}$ more in falling through the same distance (starting from rest) on two planets where the accelerations due to gravity are $2 \,\, g$ and $8 \,\,g$ respectively then $v=$