Quadratic Projectile Motion

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is given by: ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does the vertex of a parabola represent in projectile motion?

Back

The vertex of a parabola represents the maximum height of the projectile in the context of projectile motion.

Front

How do you find the maximum height of a projectile modeled by a quadratic equation?

Back

To find the maximum height, use the formula t = -b/(2a) to find the time at which the maximum height occurs, then substitute this time back into the height equation.

Front

What is the significance of the coefficient of t² in the height equation?

Back

The coefficient of t² determines the direction of the parabola: if it is negative, the parabola opens downward, indicating a maximum height.

Front

What is the formula for the height of a projectile at time t?

Back

The height h at time t can be modeled by the equation h = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

What does the term 'initial velocity' mean in the context of projectile motion?

Back

Initial velocity is the speed at which the projectile is launched at the beginning of its motion.

Front

What is the role of gravity in projectile motion?

Back

Gravity acts as a constant downward force, affecting the projectile's height and causing it to eventually fall back to the ground.

Front

How can you determine the time of flight for a projectile?

Back

The time of flight can be determined by finding the values of t when the height h = 0 in the height equation.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a) for the quadratic equation.

Front

What is the maximum height of a dolphin jumping with an initial velocity of 16 ft/s modeled by h = -16t² + 80t?

Back

The maximum height is 100 feet.