Projectiles launced horizontally

The key for the analysis is to break the motion into the vertical component and horizontal component.

?y = v_iyt + 1/2 a_yt² = 1/2 gt², because v_iy=0 and a_y = g

?x = v_ixt + 1/2 a_xt² = v_ixt, because a_x = 0

Projectiles launced at an angle

The key for the analysis is to break the motion into the vertical component and horizontal component.

v_ix = v cos? and v_iy = v sin?

V_y = v_iy + at

v_iy - gt_up = 0

t_up = v_iy/g

?y = v_iyt + 1/2 at²

?y_max = v_iyt_up - 1/2 g(t_up)² = 1/2 (v_iy²/g)

Uniform circular motion

The direction of the acceleration (the centripetal acceleration) is toward the center of the circule and its magnitude is a_c = v² / r, where v is velocity and r is radius of the circle.

For uniform circular motion: magnitude of velocity v = 2?r / T, where r is radius and T is period (in seconds).

Period T = 1/f, where f is frequency.

a_c = 4?²r / T², where r is radius and T is period.

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