Projectile Motion and Quadratics

Front

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

Back

The height can be modeled by the equation h(t) = -16t^2 + vt + h0, where v is the initial velocity and h0 is the initial height.

Front

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

Back

The vertex represents the maximum height of the projectile.

Front

How do you find the x-coordinate of the vertex in a quadratic equation?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation ax^2 + bx + c.

Front

What is the significance of the y-intercept in a projectile motion equation?

Back

The y-intercept represents the initial height from which the object is launched.

Front

What is the formula to calculate the time when a projectile hits the ground?

Back

Set the height equation h(t) = 0 and solve for t.

Front

What is the maximum height of a projectile?

Back

The maximum height is the y-coordinate of the vertex of the parabola representing the projectile's path.

Front

How does the initial velocity affect the trajectory of a projectile?

Back

A higher initial velocity results in a higher maximum height and a longer time in the air.

Front

What is the role of gravity in projectile motion?

Back

Gravity acts as a constant downward acceleration, affecting the height and time of flight.

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

How do you determine the time to reach maximum height?

Back

The time to reach maximum height is found using t = -b/(2a) from the height equation.