Answer to Question #343090 in Physics for sss

Question

An object is projected from the ground with an initial velocity of 28.5m/s at 35⁰ above the horizontal. Find the following:

(a) horizontal and vertical components of its initial velocity,

(b) time to reach the maximum height,

(c) time of flight,

(d) maximum height,

(e) the speed at the maximum height

(f) range, and

(g) velocity upon striking the ground.

Answer 1

Given:

$v_0=28.5\:\rm m/s$

$\theta=35^\circ$

$g=9.8\:\rm m/s^2$

(a)

$$v_{0x}=v_0\cos\theta=28.5\cos35^\circ=23.3\:\rm m/s$$

$$v_{0y}=v_0\sin\theta=28.5\sin35^\circ=16.3\:\rm m/s$$

(b)

$$t_1=\frac{v_{0y}}{g}=\frac{16.3}{9.8}=1.66\:\rm s$$

(c)

$$t_2=2t_1=2*1.66=3.32\:\rm s$$

(d)

$$h_{\max}=\frac{v_{0y}^2}{2g}=\frac{16.3^2}{2*9.8}=13.6\:\rm m$$

(e)

$$v=v_{0x}=23.3\:\rm m/s$$

(f)

$$R=v_{0x}t_2=23.3*3.32=77.4\:\rm m$$

(g)

$$v_{fx}=v_{0x}=23.3\:\rm m/s$$

$$v_{fy}=-v_{0y}=-16.3\:\rm m/s$$