Final answer:
The height of the firecracker after 2 seconds is 0 meters.
Step-by-step explanation:
When a firecracker is shot straight up into the air with an initial velocity of 20 m/s, we can use the equation v² = v₀² - 2a(y - y₀) to find its height after 2 seconds. In this equation, v is the final velocity, v₀ is the initial velocity, a is the acceleration, y is the final height, and y₀ is the initial height.
Given that the acceleration due to gravity (a) is -10 m/s² and the initial velocity (v₀) is 20 m/s, we can substitute these values into the equation, along with the time (t) of 2 seconds, to solve for the height (y).
Using the formula, we get:
y = y₀ + v₀t + (1/2)at²
Plugging in the values, we have:
y = 0 + (20 m/s)(2 s) + (1/2)(-10 m/s²)(2 s)²
Simplifying the equation gives:
y = 20 m + (-20 m)
So, the height of the firecracker after 2 seconds is 0 meters.