Answer to Question #311132 in Physics for 4rme

Question

An object has a launch velocity of 30.0 m/s at launch angle of 30.00 relative to horizontal. Find the a) x and y component of initial velocity, b) time to reach the peak c) total time of flight, d) vertical height to reach the peak, and e) horizontal distance. 

Answer 1

a)

$$v_{0x}=v_0\cos\theta\\ =30.0\cos30.0^\circ=26.0\:\rm m/s$$

$$v_{0y}=v_0\sin\theta\\ =30.0\sin30.0^\circ=15.0\:\rm m/s$$

b)

$$t_1=\frac{v_{0y}}{g}=\frac{26.0}{9.81}=2.65\:\rm s$$

c)

$$t_2=\frac{2v_{0y}}{g}=\frac{2*26.0}{9.81}=5.30\:\rm s$$

d)

$$h_{\max}=\frac{v_{0y}^2}{2g}=\frac{26.0^2}{2*9.81}=34.5\:\rm m$$

e)

$$R=v_{0x}t_2=15.0*5.30=79.5\:\rm m$$