Question

Equation of trajectory of a projectile is given by $y=-x^2+10x$ where x and y are in meters and x is along horizontal and y is vertically upward and particle is projected from origin. Then which of the following options is/are correct. $(g=10m/s^2)$.

• A. Initial velocity of particle is $\sqrt{505}$ m/s
• B. Horizontal range is $10m$
• C. Maximum height is $25m$
• D. Angle of projection with horizontal is ${\tan }^{-1}\left(5\right)$

Answer 1

Answer: (A)

Initial velocity of particle is $\sqrt{505}$ m/s

$y=-x^2+10x$

Comparing with Standard equation of trajectory $y=tan\theta x-\frac{g{x}^2}{2u^{2}co{s}^2\theta }$

We get $tan\theta =10$ and $\frac{g}{2u^{2}co{s}^2\theta }=1$

cos$\theta =\frac{1}{\sqrt{101}}$

u=$\sqrt{505}$m/s