Physics GRE-Classical Mechanics-Kinematics

Kinematics

Problems

PGRE1777(49)
PGRE9677(22)
PGRE9277(44)
PGRE8677(6, 8)
PGRE0177(24)

Formulas

$$v=at+v_0$$

$$x=\frac{1}{2}at^2+v_0t$$

$$v^2-v^2_0=2a\Delta x$$

Projectile Motion

$$y=v_0 \sin{(\theta)} t -\frac{1}{2}gt^2$$

$$x=v_0 \cos{(\theta)}t$$

From them

$$y=\tan{(\theta)}x-\frac{g}{2v_0^2 \cos^2{(\theta)}}x^2$$

Differentiate this

$$\frac{dy}{dx}=\tan{(\theta)}-\frac{g}{v_0^2 \cos^2{\theta}}=0$$

Isolate x

$$x=\frac{v^2_0 \sin{\theta} \cos{\theta}}{g}$$

Substitute this into x in y

$$y=\frac{v^2_0 \cos^2{\theta} \tan^2{\theta}}{2g}$$