Скачать или смотреть Projectile Motion From a Balcony: When Does It Hit the Ground and What Is the Max Height?

In this video, we solve a projectile motion word problem where a ball is thrown upward from a balcony and its height is modeled by a quadratic equation. We use algebra to find two key things:

when the ball hits the ground, and

the maximum height it reaches.

To find when the ball hits the ground, we set the height equation equal to zero and solve for time using the quadratic formula. This gives two time values, but one is negative, so we discard it because time cannot be negative. The remaining positive solution tells us the ball hits the ground at about 2.58 seconds.

To find the maximum height, we use the vertex method. The time of maximum height comes from the vertex formula t = -b/(2a). After finding that time, we plug it back into the height equation to compute the maximum height.

Skills covered:

Modeling height with a quadratic

Using the quadratic formula for time

Discriminant and root meaning

Vertex time and maximum height

More algebra and physics style word problems:
mathgpt.today/math-solver
mathgpt.today/problems
mathgpt.today/video
mathgpt.today/calculators