Question

Which one of the following statements is not true about the motion of a projectile?

• A. The time of flight of a projectile is proportional to the speed with which it is projected at a given angle of projection.
• B. The horizontal range of a projectile is proportional to the square root of the speed with which it is projected, at a given angle of projection
• C. For a given speed of projection, the angle of projection for maximum range is ${45}^{\circ }$
• D. At maximum height, the acceleration due to gravity is perpendicular to the velocity of the projectile

Answer 1

The correct option is B The horizontal range of a projectile is proportional to the square root of the speed with which it is projected, at a given angle of projection

Since, $T=\frac{2u\sin \theta }{g}\Rightarrow T\propto u....\left(1\right)$
$\therefore$ Time of flight is proportional to the initial velocity of projectile
$R=\frac{u^2\sin 2\theta }{g}\Rightarrow R\propto u^2....\left(2\right)$
So, $R$ is not proportional to the square root of initial velocity of projectile. Range will be maximum for $\theta ={45}^{\circ }$ because $\sin 2\theta$ will become $1$ (i.e. maximum).

At highest point only horizontal component of velocity exits so velocity at the highest point is perpendicular to the acceleration due to gravity.