Answer to Question #180644 in Mechanics | Relativity for Peter

Question

Suppose a large rock is ejected from a volcano with a speed of 25m/s and at an angle of 35degree above the horizontal. If the rock strikes the side of the volcano at an altitude 20m lower than the starting point. What are the magnitude and direction of the rock s velocity at impact?

Answer 1

$v_x=vcos\alpha=20.48~\frac ms,$

$v_y=vsin\alpha=14.34~\frac ms;$

$u_x=v_x=20.48~\frac ms,$

$g=\frac{u_y^2-v_y^2}{2h}\implies$

$u_y=\sqrt{2gh+v_y^2}=24.45~\frac ms,$

$u=\sqrt{u_x^2+u_y^2}=31.89~\frac ms,$

$\beta=atan\frac{u_y}{u_x}=50°.$