Question

list all formulas related to projectile motion required for jee mains

Answer 1

1. $u_x = u \cos\theta, \; u_y = u \sin\theta$

2. $x = u \cos\theta \, t$

3. $y = u \sin\theta \, t - \frac{1}{2} g t^2$

4. $T = \frac{2u\sin\theta}{g}$

5. $H = \frac{u^2 \sin^2\theta}{2g}$

6. $R = \frac{u^2 \sin(2\theta)}{g}$

7. $t_{\text{max}} = \frac{u\sin\theta}{g}$

8. $y = x\tan\theta - \frac{g x^2}{2u^2\cos^2\theta}$

9. $v_y = u\sin\theta - gt$

10. $v = \sqrt{(u\cos\theta)^2 + (u\sin\theta - gt)^2}$

Answer 2

Below is a list of the key formulas for projectile motion that you need to know for JEE Mains:

1. Decomposition of the initial velocity:

   $$u_x = u \cos\theta,\quad u_y = u \sin\theta$$

2. Horizontal displacement:

   $$x = u \cos\theta \, t$$

3. Vertical displacement:

   $$y = u \sin\theta \, t - \frac{1}{2} g t^2$$

4. Time of flight (total time in air):

   $$T = \frac{2u\sin\theta}{g}$$

5. Maximum height attained:

   $$H = \frac{u^2\sin^2\theta}{2g}$$

6. Range of the projectile:

   $$R = \frac{u^2\sin(2\theta)}{g}$$

7. Time to reach maximum height:

   $$t_{\text{max}} = \frac{u\sin\theta}{g}$$

8. Trajectory equation (path of the projectile):

   $$y = x\tan\theta - \frac{g x^2}{2u^2\cos^2\theta}$$

9. Vertical component of velocity at any time $t$:

   $$v_y = u\sin\theta - gt$$

10. Speed at any time $t$ (combining horizontal and vertical components):

    $$v = \sqrt{(u\cos\theta)^2 + (u\sin\theta - gt)^2}$$

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Explanation (Minimal and to the point):

• Step 1: Resolve the initial velocity into horizontal ($u\cos\theta$) and vertical ($u\sin\theta$) components.
• Step 2: Use horizontal motion $x = u\cos\theta\, t$ (with no acceleration) and vertical motion $y = u\sin\theta\, t - \frac{1}{2}gt^2$ (with gravitational acceleration) to derive other quantities.
• Step 3: Derive key quantities like time of flight, maximum height, and range using the condition when vertical displacement or velocity at the peak becomes zero.
• Step 4: Combine the component formulas to form the trajectory equation and determine the speed at any time.