A projectile is launched with an initial speed of $40 \mathrm{~m} / \mathrm{s}$ at an angle $30^{\circ}$ above the ground. The projectile lands on a hillside 2.0 s later. The net displacement from where the projectile lands on hillside 2.0 s later. The net displacement from where the projectile was launched to where it hits the target is (take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A ball is projected with a velocity $5 \mathrm{~m} / \mathrm{s}$, so that its horizontal range is twice the greatest height attained. The value of range is

A point moves in the $x y$-plane according to the following equation, $x=a \sin \omega t, y=a(1-\cos \omega t)$, where $a$ and $\omega$ are positive constants. Find the angle between the point's velocity and acceleration vectors.

A particle of mass $m=1 \mathrm{~kg}$ moves in the $x y$-plane. The force on it at time $t$ is $F(t)=[2 \sin (\alpha t) \hat{\mathbf{i}}+3 \cos (\alpha t) \hat{\mathbf{j}}] \mathrm{N}$, where $\alpha=1 \mathrm{~s}^{-1}$. At time $t=0$, the particle is at rest at the origin. Calculate the magnitude of its position vector $\mathbf{r}$ (in m ) and velcoity vector $\mathbf{v}$ (in m/s) at time $t=\frac{\pi}{2} \mathrm{~s}$.