Projectile Motion (Quadratics)

Front

What is projectile motion?

Back

Projectile motion is the motion of an object thrown into the air, subject to the force of gravity, which follows a curved path called a parabola.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does the variable 'h(t)' represent in projectile motion equations?

Back

In projectile motion equations, 'h(t)' represents the height of the object at time 't'.

Front

What is the formula for the height of an object in projectile motion?

Back

The height of an object in projectile motion can be modeled by the equation h(t) = -gt² + v₀t + h₀, where g is the acceleration due to gravity, v₀ is the initial velocity, and h₀ is the initial height.

Front

How do you find the maximum height of a projectile?

Back

The maximum height of a projectile can be found using the vertex formula: h = -b/(2a) for the equation h(t) = at² + bt + c.

Front

What is the significance of the vertex in a parabola?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, indicating the highest or lowest height of the projectile.

Front

What is the acceleration due to gravity?

Back

The acceleration due to gravity is approximately 9.8 m/s² (or 32 ft/s²) and acts downward on the projectile.

Front

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

Back

The time of flight can be determined by solving the equation h(t) = 0 for t, which gives the total time the projectile is in the air.

Front

What is the formula to calculate the height of a projectile at a specific time?

Back

To calculate the height of a projectile at a specific time, substitute the value of 't' into the height equation h(t) = -gt² + v₀t + h₀.

Front

What is the effect of initial velocity on projectile motion?

Back

The initial velocity affects how high and how far the projectile will travel; a higher initial velocity results in a greater range and height.