Motion in a Plane

The trajectory of projectile, projected from the ground is given by \(y=x-\frac{{x}^{2}}{20}\). Where x and y are measured in meter. The maximum height attained by the projectile will be:

A bullet is fired from a gun at the speed of \(280{\mathrm{ms}}^{-1}\) in the direction \(30^\circ\) above the horizontal. The maximum height attained by the bullet is \(\left(\mathrm{g}=9.8{\mathrm{ms}}^{-2},\sin 30^\circ =0.5\right)\):-

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

A car starts from rest and accelerates at \( 5 \mathrm{~m} / \mathrm{s}^{2} \). At \( \mathrm{t}=4 \mathrm{~s} \), a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at \( \mathrm{t}=6 \mathrm{~s} \) ?

[NEET 2021]

A particle moving in a circle of radius \( \mathrm{R} \) with a uniform speed takes a time \( \mathrm{T} \) to complete one revolution. If this particle were projected with the same speed at an angle \( \theta \) to the horizontal, the maximum height attained by it equals \( 4 \mathrm{R} \). The angle of projection, \( \theta \), is then given by:

[NEET 2021]