Projectile Motion & Mixed Review Quadratics

Front

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

Back

The height, h, of an object in projectile motion can be modeled by the quadratic function: h(t) = -16t^2 + vt + h0, where v is the initial velocity and h0 is the initial height.

Front

How do you find the maximum height of a projectile?

Back

To find the maximum height of a projectile, determine the vertex of the quadratic function representing its height. The time at which the maximum height occurs is given by t = -b/(2a) for the function h(t) = at^2 + bt + c.

Front

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

Back

The vertex of a parabola in projectile motion represents the maximum height of the projectile and the time at which it reaches that height.

Front

What is the quadratic formula?

Back

Front

How do you solve a quadratic equation by taking square roots?

Back

To solve a quadratic equation of the form ax^2 = k, isolate x^2 and then take the square root of both sides: x = ±√(k/a).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant, given by b^2 - 4ac, determines the nature of the roots of the quadratic equation: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is the initial height in the function h(t) = -16t^2 + 64t + 960?

Back

The initial height is the value of h when t = 0, which is h(0) = 960 meters.

Front

How do you determine the time it takes for a projectile to reach its maximum height?

Back

The time to reach maximum height can be found using t = -b/(2a) from the quadratic function h(t) = at^2 + bt + c.

Front

What is the maximum height of the projectile modeled by h(t) = -16t^2 + 64t + 960?

Back

The maximum height can be found by calculating the vertex of the parabola, which is 1024 meters.

Front

What is the height of the object after 5 seconds in the function h(t) = -16t^2 + 70t + 95?

Back

To find the height after 5 seconds, substitute t = 5 into the function: h(5) = -16(5)^2 + 70(5) + 95 = 45 feet.