Rocket Motion and Height Analysis

The video tutorial explains how to determine the maximum height and splashdown time of a rocket launched by NASA. It uses a quadratic function to model the rocket's height over time and employs both graphical and algebraic methods to find the vertex and T-intercepts. The tutorial demonstrates using Desmos for graphical analysis and the quadratic formula for calculations, ultimately verifying the results through graph inspection.

What is the initial height of the rocket above sea level?

• 108 meters

• 0 meters

• 277 meters

• 4,022.74 meters

Which tool is used to graphically analyze the height function?

• Desmos

• Mathematica

• GeoGebra

• Excel

What is the formula used to find the time at which the rocket reaches its maximum height?

• T = -B / 2A

• T = -B / A

• T = B / 2A

• T = B / A

Why is it important to use the exact value of T rather than a rounded value when calculating maximum height?

• To save time

• To reduce error

• To simplify calculations

• To avoid using a calculator

What is the approximate maximum height reached by the rocket?

• 2,000 meters

• 5,000 meters

• 3,500 meters

• 4,022.74 meters

What equation is used to determine the time of splashdown?

• H(T) = 277

• H(T) = 108

• H(T) = 4,022.74

• H(T) = 0

Which mathematical method is used to solve for the time of splashdown?

• Factoring

• Graphical estimation

• Completing the square

• Quadratic formula

What is the approximate time it takes for the rocket to splash down?

• 150 seconds

• 56.92 seconds

• 100 seconds

• 28.27 seconds

Why is one of the solutions for the time of splashdown discarded?

• It is not realistic

• It is not a whole number

• It is negative

• It is too large

What feature of Desmos helps verify the calculated key points on the graph?

• Grade points

• Axis labels

• Grid lines

• Color coding