A displacement is a signed distance from a reference level. In a quadratic flight model, check whether that level is the ground or somewhere else before writing the landing equation. Then use a Desmos regression to find the time and keep only a time after launch. Setting displacement to zero can find a return to the starting height rather than a landing.
Hints
- Hint 1
A displacement tells you how far above or below a reference level the ball is. The roof is the reference level here. What displacement represents the ground, feet below it?
- Hint 2
An equation with a squared time can have two solutions, including one before launch. After you write the equation for ground level, how will you keep only a time that occurs after launch?
Step-by-step
Match the ground's displacement, then solve
Step 1Find the displacement at ground level
A displacement is a signed distance from the rooftop. The ground is feet below the roof, so ground level means . Zero displacement would put the ball at rooftop height, not on the ground.
- Step 2
Write the landing equation
Replace with the given model in : . This asks when the modeled displacement reaches the ground's level.
- Step 3
Solve for a time after launch
Type . Desmos uses for the unknown time; asks it to match the two sides, and the braces keep only positive time. Under PARAMETERS, Desmos reports . Since , the ball hits the ground seconds after launch. Choice A.