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 variable 'h' represent in the context of projectile motion equations?

Back

In projectile motion equations, 'h' represents the height of the object above a reference point, typically the ground.

Front

What is the significance of the coefficient of t² in a quadratic equation modeling projectile motion?

Back

The coefficient of t² (usually negative) indicates the acceleration due to gravity, affecting how quickly the object falls.

Front

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

Back

The maximum height can be found using the vertex formula: t = -b/(2a), where a and b are coefficients from the equation h(t) = at² + bt + c.

Front

If a dolphin jumps with an initial velocity of 16 feet per second, what does this represent in the equation h = -16t² + 80t?

Back

The initial velocity of 16 feet per second is represented by the coefficient of t in the equation, which affects the height over time.

Front

What does the term 'projectile motion' refer to?

Back

Projectile motion refers to the motion of an object that is thrown or projected into the air, subject to the force of gravity.

Front

In the equation h(t) = -16t² + 80t, what does the '80' represent?

Back

The '80' represents the initial height from which the dolphin jumps, measured in feet.

Front

What is the formula to calculate the time it takes for a projectile to hit the ground?

Back

To find the time it takes for a projectile to hit the ground, set h(t) = 0 and solve for t in the quadratic equation.

Front

What is the role of gravity in projectile motion?

Back

Gravity acts as a constant downward force, affecting the trajectory and speed of the projectile over time.

Front

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

Back

The time of flight can be determined by finding the roots of the quadratic equation, which represent when the height is zero.