A projectile is projected at $$30^{\circ}$$ from horizontal with initial velocity $$40 \mathrm{~ms}^{-1}$$. The velocity of the projectile at $$\mathrm{t}=2 \mathrm{~s}$$ from the start will be : (Given $$g=10 \mathrm{~m} / \mathrm{s}^{2}$$ )

A body of mass $$500 \mathrm{~g}$$ moves along $$\mathrm{x}$$-axis such that it's velocity varies with displacement $$\mathrm{x}$$ according to the relation $$v=10 \sqrt{x} \mathrm{~m} / \mathrm{s}$$ the force acting on the body is:-

A space ship of mass $$2 \times 10^{4} \mathrm{~kg}$$ is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if $$g=10 \mathrm{~m} / \mathrm{s}^{2}$$ and radius of earth $$=6400 \mathrm{~km}$$ ):

When vector $$\vec{A}=2 \hat{i}+3 \hat{j}+2 \hat{k}$$ is subtracted from vector $$\overrightarrow{\mathrm{B}}$$, it gives a vector equal to $$2 \hat{j}$$. Then the magnitude of vector $$\overrightarrow{\mathrm{B}}$$ will be :