Essential Equations for Projectile Motion

Projectile motion involves equations for displacement, velocity, and acceleration.

There are four equations for constant acceleration and one for average speed.

Displacement can be used in the x or y direction, and there are three types of projectile motion trajectories.

🔢 The key equation for determining the height of a cliff is d = vt.

🌊 The range of the projectile is given by the equation range = vx * t.

🚀 To find the speed of the ball just before it hits the ground, the horizontal and vertical velocities are used.

📝 The time it takes to go from point A to point B in projectile motion is calculated using the equation t = v*sin(theta) / g.

📉 The total time it takes to go from point A to point C is twice the time it takes to go from A to B, so it can be calculated as 2*v*sin(theta) / g.

🎯 The maximum height between point A and point B can be calculated using the equation h = v^2*sin^2(theta) / (2*g).

📝 The time it takes for a ball to go from point A to point C in projectile motion is equal to 2v sine theta divided by g.

🔢 The range of a projectile can be calculated using the equation v squared sine 2 theta divided by g.

🗻 To calculate the time it takes for a ball to hit the ground when launched at an angle from a cliff, the equation y final equals y initial plus v y initial t plus one half g t squared can be used.

📝 To solve for time in projectile motion, use the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a)

🔁 An alternative way to calculate time is to use the equation: t = (v * sin(theta)) / g

📏 To find the range of the ball, use the relevant equation provided.

📝 The range of a projectile with a symmetrical trajectory can be found using the equation v_x times t.

🔢 The speed of the projectile just before it hits the ground can be determined by using the same v_x value at all points and finding the final vertical velocity using the equation v_y = v_y_initial - g * t.

📐 To find the angle of the projectile's path, use the equation theta = inverse tangent(v_y / v_x), and describe the angle as either below the horizontal or relative to the positive x-axis.

📐 Understanding and selecting the correct equations for projectile motion problems.

🌠 Equations for a projectile falling down from a cliff and traveling horizontally.

🔀 Equations for projectiles with different trajectories and finding angles and speeds.

📝 Summary of the main equations for projectile motion problems.