Answer:
t≈2 seconds,t≈38 seconds
Step-by-step explanation:
h=−16t2+ v0t
Step 1. Solve the equation.
1,200= −16t^2+ 640t
We know the velocity, v0, is 640 feet per second.
The height is 1,200 feet. Substitute the values.
This is a quadratic equation. Rewrite it in standard form. Solve the equation using the quadratic formula.
ax^2 + bx + c . = 0
16t^2 −640t + 1,200 = 0
Identify the values of a, b, and c.
a=16, b=−640, c=1,200
Write the quadratic formula.
t=−b± √b2−4ac‾‾‾‾‾‾‾‾
2a
640+ √332,800‾‾‾‾‾‾‾‾ t= √640− √332,800‾‾‾‾‾‾‾
32 32
Rewrite to show two solutions.
t=640+332,800‾‾‾‾‾‾‾‾√32,t=640−332,800‾‾‾‾‾‾‾‾√32
Approximate the answer with a calculator.
t≈2 seconds,t≈38 seconds
Step 2. Check the answer. The check is left to you.
Step 3. Answer the question.
The firework will go up and then fall back down. As the firework goes up, it will reach 1,200 feet after approximately 2 seconds. It will also pass that height on the way down at 38 seconds.
