Question

Hi guys, I'm working on a project and I'm stuck on one of the questions. If the equation for a firework being launched off the roof of a 30 foot building with an initial upward velocity of 150 ft/sec is H=-16t^2+150t+30
When will the firework land if it does not explode?

Answer 1

I assume the landing is expected to be on the ground, not on the roof.
Is the expression you are given using zero height for the ground, or is it using zero height for the launch site (the top of the roof at 30 ft height)?

Let's find out.

Look at the height at time zero, t = 0.

\(H=-16t^2+150t+30 \)

Let \(t = 0\)

\(H=-16\times0^2+150 \times 0t+30 \)

\(H = 30\)

At time zero, the height is 30 ft.
That makes sense because the problem states that the rocket is launched from the roof of a 30-ft building. It also tells us that the height of the launch is 30 ft. That means the ground, where the rocket will fall, is at 0 ft.

Since you want to know at what time the rocket falls on the ground, you are looking for the time when the height H(t) is equal to zero.

Set your expression equal to zero and solve for t.

\(-16t^2+150t+30 = 0\)

Answer 2

Thank you! I got it.

Answer 3

Great.
You're welcome.