Projectiles Questions and Answers

A particle is projected from the point O with speed 8 ms$^{-1}$ at an angle $\theta$ above the horizontal, and it passes through the point $A(8;\ -1.81)$, distances in metres, with O as origin. Taking $g=9.81$ ms$^{-2}$, there are two possible values of $\theta$. Find the smaller one, in degrees, correct to 1 decimal place.

A particle is projected from O with speed 8 ms$^{-1}$ at an angle $\theta$ above the horizontal and passes through the point $A(8;\ -1.81)$, distances in metres. The two possible values of $\theta$ are $45^{\circ}$ and $32.2^{\circ}$. Which value gives the minimum time taken to reach A, and why?

A stone is projected from a point A on level ground with a speed of 20 ms$^{-1}$ at an angle of 30° to the horizontal, towards a pole standing 30 m away. Find the time, in seconds, at which the stone is level with the pole. Give your answer correct to 3 significant figures.

A particle is projected at an angle $\theta$ above the horizontal where $\theta=\sin^{-1}\left(\dfrac{\sqrt{2}}{2}\right)$. Find $\theta$ in degrees.

The trajectory of a projectile is described by $y = 2x - 0.01x^{2}$, where x is the horizontal displacement and y is the vertical displacement from the point of projection.

A particle is projected horizontally from a point O at a height of 45 m vertically above a point P on level ground. It hits the ground at a point Q with PQ = 15 m. Take $g = 9.81$ ms$^{-2}$.