Answer:
[tex]\boxed {\boxed {\sf 2100 \ meters}}[/tex]
Explanation:
We are asked to find the distance a firework travels.
We are given the initial velocity, acceleration, and time, but we don't know the final velocity. Therefore, we will use the following kinematic equation.
[tex]d=v_it+\frac{1}{2} at^2[/tex]
The initial velocity is 235 meters per second. The firework travels for 12 seconds. It has an acceleration of -10 meters per second squared.
Substitute the values into the formula.
[tex]d= (235 \ m/s)(12 \ s) + \frac{1}{2} (-10 m/s^2)(12 \ s)^2[/tex]
Multiply the first 2 numbers in parentheses. The units of seconds cancel.
[tex]d=(235 \ m * 12 ) + \frac{1}{2} (-10 \ m/s^2)(12 \ s )^2[/tex]
[tex]d= (2820 \ m)+ \frac{1}{2} (-10 \ m/s^2)(12 \ s )^2[/tex]
Solve the exponent.
[tex]d=(2820 \ m)+ \frac{1}{2} (-10 \ m/s^2)(144 \ s^2)[/tex]
Multiply the other numbers in parentheses. The units of seconds squared cancel.
[tex]d=(2820 \ m)+ \frac{1}{2} (-10 \ m * 144 )[/tex]
[tex]d=(2820 \ m)+ \frac{1}{2} (-1440 \ m)[/tex]
Multiply by 1/2 or divide by 2.
[tex]d= 2820 \ m + (-720 \ m)[/tex]
Add.
[tex]d= 2100 \ m[/tex]
The firework traveled 2100 meters before exploding.
