Question

Here are the equations as well as a graph of 3 fireworks; the first two were shot from a 20 foot tall building, and the last was shot from the ground.

h(t)=-16t^2+100t+20
h(t)=-16t^2+150t+20
h(t)=-16t^2+160t

What can you conclude about how the height of the building and the initial
velocity of the item launched affect the maximum height and the time it
takes to get there?

Is there something I'm missing here? Am I overthinking? I get how to explain "how the height of the building.. might affect the maximum height," but I don't know how I'd explain the rest. I'm stumped.

Answer 1

Effect on Maximum Height of Building Height

The building height adds directly to the maximum height for a given launch velocity. It has no effect on the time it takes to reach the maximum height.

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Effect on Maximum Height of Initial Velocity

Since acceleration is constant, the vertical velocity decreases at a constant rate. The time it takes to reach zero (time to maximum height) is directly proportional to the initial velocity.

The maximum height is jointly proportional to the initial velocity and the time it takes to reach the maximum height. That is, the maximum height is proportional to the square of the initial velocity.