Projectile Motion and Graphical Analysis

The video tutorial addresses a classic physics problem involving a projectile shot vertically with given initial velocity and height. The task is to find when the projectile reaches 170 feet above the ground. The problem is analyzed graphically using Desmos and solved algebraically using the quadratic formula. The solutions are verified graphically, showing the projectile reaches the height at approximately 0.33 seconds on the way up and 9.23 seconds on the way down.

What is the initial velocity of the projectile in the problem?

• 200 feet per second

• 121 feet per second

• 153 feet per second

• 170 feet per second

What is the initial height from which the projectile is launched?

• 100 feet

• 150 feet

• 121 feet

• 170 feet

Why was the variable 'y' used instead of 'h' in the graphical representation?

• To avoid confusion with other variables

• To match the standard form of equations

• Because Desmos does not graph 'h'

• To simplify the equation

What is the purpose of setting the equation equal to zero in the algebraic solution?

• To find the maximum height

• To determine the time of flight

• To solve for the time when the height is 170 feet

• To calculate the initial velocity

Which mathematical method is used to solve the equation for time in this problem?

• Graphical analysis

• Quadratic formula

• Completing the square

• Factoring

What are the two times when the projectile reaches a height of 170 feet?

• 0.33 seconds and 9.23 seconds

• 1.23 seconds and 8.33 seconds

• 2.33 seconds and 7.23 seconds

• 3.33 seconds and 6.23 seconds

What is the significance of the plus/minus sign in the quadratic formula solution?

• It shows two possible times

• It indicates two possible velocities

• It represents two different heights

• It denotes two different angles

How can the solution be verified graphically?

• By comparing with a linear graph

• By measuring the area under the curve

• By finding the intersection points with y=170

• By checking the slope of the graph

What tool is used to graphically verify the solution?

• Desmos

• Matlab

• Excel

• Python

What is the first value of the ordered pair in the graphical verification?

• The initial height

• The height of the projectile

• The time when the projectile is at 170 feet

• The initial velocity