Question

A firework rocket is shot upward at a rate of 640ft/sec. Use the projectile formula h= -16t^2 +v0t to determine the times when the height of the firework will be 1,200 feet. Round your answer to the nearest whole number.

Answer 1

t≈2 seconds,t≈38 seconds

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.

Answer 2

2 seconds and 38 seconds

Explanation:

h=-16t²-vot

1,200=-16t²-640t

turn this into standard form

16t²-640t+1200=0

now plug thes numbers into the quadratice formula

a 16 b -640 c 1200

solve with quadratic formula to get ≅2 and ≅38 seconds