A projectile fired with initial velocity $u$ at some angle $\theta $ has a range $R$. If the initial velocity be doubled at the same angle of projection, then the range will be
$2R$
$R/2$
$R$
$4R$
An insect trapped in a circular groove of radius $12 \;cm$ moves along the groove steadily and completes $7$ revolutions in $100\; s$.
$(a)$ What is the angular speed, and the linear speed of the motion?
$(b)$ Is the acceleration vector a constant vector ? What is its magnitude ?
A truck is moving on the horizontal road with constant speed $v.$ A ball is thrown from the truck vertical up at speed $u$ $w.r.t.$ truck. What is distance traversed by the truck when ball returns on the truck
A hill is $500\, m$ high. Supplies are to be sent across the hill, using a canon that can hurl packets at a speed of $125 \,m/s$ over the hill. The canon is located at a distance of $800 \,m$ from the foot of hill and can be moved on the ground at a speed of $2\, ms^{-1}$; so that its distance from the hill can be adjusted. What is the shortest time in which a packet can reach on the ground across the hill ? Take, $g = 10\, ms^{-2}$.
A projectile is fired from level ground at an angle $\theta $ above the horizontal. The elevation angle $\phi $ of the highest point as seen from the launch point is related to $\theta $ by the relation
If the time of flight of a bullet over a horizontal range $R$ is $T$, then the angle of projection with horizontal is ......