All Flashcards
Steps to find the time to reach max height in projectile motion?
1: Use v_y = v₀ * sin(θ) - gt. 2: Set v_y = 0 at max height. 3: Solve for t: t = (v₀ * sin(θ)) / g.
Steps to analyze projectile motion problems?
1: Identify knowns and unknowns. 2: Break motion into x and y components. 3: Apply appropriate kinematic equations. 4: Solve for unknowns.
Steps to solve for range of a projectile?
1: Find the time of flight. 2: Use the horizontal velocity component. 3: Calculate range using x = v_x * t.
Steps to find the maximum height of a projectile?
1: Find the time to reach the maximum height. 2: Use the vertical kinematic equation y = v₀ * sin(θ) * t - 1/2 * gt². 3: Substitute the time to find the maximum height.
Steps to use calculus to find velocity from a position function?
1: Differentiate the position function with respect to time. 2: The result is the velocity function.
Steps to use calculus to find displacement from a velocity function?
1: Integrate the velocity function with respect to time. 2: Evaluate the integral between the initial and final times.
Label the components of initial velocity in projectile motion.
1: v₀ (Initial Velocity), 2: v₀ * cos(θ) (Horizontal Component), 3: v₀ * sin(θ) (Vertical Component), 4: θ (Launch Angle)
Label the forces acting on a projectile during its motion (ignoring air resistance).
1: Force of Gravity (downwards)
What is the effect of gravity on the vertical velocity of a projectile?
Causes the vertical velocity to decrease as the object rises and increase as it falls.
What happens when the vertical velocity (v_y) is zero in projectile motion?
The projectile reaches its maximum height.
What is the effect of increasing the launch angle (θ) on the range of a projectile (given constant initial speed)?
Increases the range up to a maximum at 45 degrees, then decreases it.
What is the effect of increasing initial velocity on range?
Range increases.
What happens to the horizontal velocity of a projectile (ignoring air resistance)?
It remains constant throughout the motion.