A projectile can have the same range $$'R\,'$$ for two angles of projection. If $$'{T_1}'$$ and $$'{T_2}'$$ to be time of flights in the two cases, then the product of the two time of flights is directly proportional to.
A.
$$R$$
B.
$$\frac{1}{R}$$
C.
$$\frac{1}{{{R^2}}}$$
D.
$${R^2}$$
Answer :
$$R$$
Solution :
The angle for which the ranges are same is complementary.
Let one angle be $$\theta ,$$ then other is $${90^ \circ } - \theta $$
$$\eqalign{
& {T_1} = \frac{{2u\,\sin \theta }}{g},\,\,\,{T_2} = \frac{{2u\,\cos \theta }}{g} \cr
& {T_1}{T_2} = \frac{{4{u^2}\,\sin \theta \cos \theta }}{g} = 2R\,\,\,\left( {\because R = \frac{{{u^2}{{\sin }^2}\theta }}{g}} \right) \cr} $$
Hence it is proportional to $$R.$$
Releted MCQ Question on Basic Physics >> Kinematics
Releted Question 1
A river is flowing from west to east at a speed of $$5$$ metres per minute. A man on the south bank of the river, capable of swimming at $$10$$ metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction-
A boat which has a speed of $$5 km/hr$$ in still water crosses a river of width $$1 \,km$$ along the shortest possible path in $$15 \,minutes.$$ The velocity of the river water in $$km/hr$$ is-
In $$1.0\,s,$$ a particle goes from point $$A$$ to point $$B,$$ moving in a semicircle of radius $$1.0 \,m$$ (see Figure). The magnitude of the average velocity-
A ball is dropped vertically from a height $$d$$ above the ground. It hits the ground and bounces up vertically to a height $$\frac{d}{2}.$$ Neglecting subsequent motion and air resistance, its velocity $$v$$ varies with the height $$h$$ above the ground as-