Answer to Question #292356 in Physics for Felco

Question

A ball is thrown making an angle of 30 degrees above the horizontal with a velocity of 20m/s from the top of a building 50m high. Calculate

(i) The time of flight (ii) The horizontal range. (iii) The velocity with which it hits the ground. (g= 10m/s²)

Answer 1

(g=9.8 m/s²)

(i) The time of flight:

$$t_{up}=\dfrac{v\sin\theta}{g},\space t_{down}=\sqrt{\dfrac{2[h+v^2\sin^2\theta/(2g)]}{g}},\\\space\\ T=t_{up}+t_{down}=4.05\text{ s}.$$

(ii) The horizontal range:

$$R=v\cos\theta·T=70.2\text{ m}.$$

(iii) The velocity with which it hits the ground.

$$u=\sqrt{(v\cos\theta)^2+2g[h+v^2\sin^2\theta/(2g)]}=\\=37\text{ m/s}^2.$$