Answer to Question #181658 in Physics for Autumn

Question

An object is projected from the ground with an initial velocity of 24.5 m/s at 30o above the horizontal.

Find the (a) horizontal and vertical components of its initial velocity, (b) time to reach the maximum

height, (c) time of flight, (d) maximum height attained by the object, (e) speed at the maximum height,

(f) range, and the (g) velocity upon striking the ground.

Answer 1

(a) horizontal and vertical components of its initial velocity

$$v_y=v\sin\theta=12.3\text{ m/s},\\ v_x=v\cos\theta=21.2\text{ m/s}.$$

(b) time to reach the maximum height

$$t=\frac{v_y}{g}=1.26\text{ s}.$$

(c) time of flight

$$T=2t=2.52\text{ s}.$$

(d) maximum height attained by the object

$$h_\text{max}=\frac{v_y^2}{2g}=30.6\text{ m}.$$

(e) speed at the maximum height

$$v_h=v_x=21.2\text{ m/s}.$$

(f) range

$$R=Tv_x=53.4\text{ m/s}.$$

(g) velocity upon striking the ground

$$v_s=v=24.5\text{ m/s}.$$