What does the quadratic function $$h(t) = -16t^2 + v_ot + h_o$$ represent in vertical motion?

This function models the height (h) of an object in free fall or projectile motion, where $$v_o$$ is the initial velocity and $$h_o$$ is the initial height.

What is the initial height in a vertical motion problem?

The initial height is the height from which an object is thrown or dropped, represented by $$h_o$$ in the quadratic equation for vertical motion.

How do you determine the time it takes for a projectile to hit the ground?

Set the height equation $$h(t) = 0$$ and solve for t using the quadratic formula. This gives the time at which the projectile reaches ground level.

What is the maximum height reached by a projectile?

The maximum height is found by evaluating the height function at the vertex time, which can be calculated using the vertex formula $$t = -\frac{b}{2a}$$ .

What is the difference between the y-intercept and the vertex of a parabola?

The y-intercept is the point where the parabola crosses the y-axis (when $$x = 0$$ ), while the vertex is the highest or lowest point of the parabola.

What does it mean for a quadratic function to have a maximum point?

A quadratic function has a maximum point if it opens downwards (the coefficient of $$x^2$$ is negative), indicating that the vertex is the highest point on the graph.

How can you verify if a given maximum height is reasonable in a vertical motion problem?

Check if the maximum height is consistent with the initial height and the time of flight. It should not exceed the height calculated from the initial conditions.

What is the relationship between time and height in vertical motion?

In vertical motion, height is a function of time, typically represented by a quadratic equation, showing how height changes as time progresses.

What is the role of initial velocity in determining the motion of a projectile?

Initial velocity affects how high and how far a projectile will travel. A higher initial velocity results in a greater maximum height and longer flight time.

Vertical Motion Assignment Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the process of completing the square for a quadratic expression?

Back

2.

FLASHCARD QUESTION

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of a parabola, depending on its orientation. It represents the maximum or minimum value of the quadratic function.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

How do you find the maximum height of a projectile?

Back

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

What does it mean if a quadratic function opens upwards?

Back

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