Question

a hill is located 25 m above ground level and a ball is thrown at an angle of 30° above horizontal at a velocity of 50 m/s. calculate where along the x axis the ball will land on the hill.

Answer 1

The equation of trajectory of a projectile

$$y=y_0+x \tan(\theta)-\frac{gx^2}{2v_0^2\cos^2(\theta)}$$

At the surface of ground $y=0,$ hence

$$0=25+x \tan(30\degree)-\frac{9.8x^2}{2\times 50^2\cos^2(30\degree)}$$

Root

$$x=37\:\rm m$$