The equation of a projectile is $y=a x-b x^2$. Its horizontal range is ......
$\frac{a}{b}$
$\frac{b}{a}$
$a+b$
$b-a$
Two particles are projected simultaneously in the same vertical plane, from the same point on ground, but with same speeds but at different angles $( < 90^o )$ to the horizontal. The path followed by one, as seen by the other, is
A particle starts from the origin at $t=0$ $s$ with a velocity of $10.0 \hat{ j } \;m / s$ and moves in the $x-y$ plane with a constant acceleration of $(8.0 \hat{ i }+2.0 \hat{ j }) \;m \,s ^{-2} .$
$(a)$ At what time is the $x$ - coordinate of the particle $16\; m ?$ What is the $y$ -coordinate of the particle at that time?
$(b)$ What is the speed of the particle at the time?
The position of a particle is given by
$r=3.0 t \hat{i}+2.0 t^{2} \hat{j}+5.0 \hat{k}$
where $t$ is in seconds and the coefficients have the proper units for $r$ to be in metres.
$(a)$ Find $v (t)$ and $a (t)$ of the particle.
$(b)$ Find the magnitude and direction of $v (t)$ at $t=1.0 s$
A particle moves with constant speed $v$ along a regular hexagon $ABCDEF$ in the same order. Then the magnitude of the average velocity for its motion from $A$ to