Question

If a firework has an initial velocity of 235m/s and is in the air for 12 seconds with an acceleration of -10 m/s2 before exploding, how far did it go?

Answer 1

Answer:

$\boxed {\boxed {\sf 2100 \ meters}}$

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.

$d=v_it+\frac{1}{2} at^2$

The initial velocity is 235 meters per second. The firework travels for 12 seconds. It has an acceleration of -10 meters per second squared.

• $v_i$= 235 m/s
• t= 12 s
• a= -10 m/s²

Substitute the values into the formula.

$d= (235 \ m/s)(12 \ s) + \frac{1}{2} (-10 m/s^2)(12 \ s)^2$

Multiply the first 2 numbers in parentheses. The units of seconds cancel.

$d=(235 \ m * 12 ) + \frac{1}{2} (-10 \ m/s^2)(12 \ s )^2$

$d= (2820 \ m)+ \frac{1}{2} (-10 \ m/s^2)(12 \ s )^2$

Solve the exponent.

• (12 s)²= 12 s * 12s = 144 s²

$d=(2820 \ m)+ \frac{1}{2} (-10 \ m/s^2)(144 \ s^2)$

Multiply the other numbers in parentheses. The units of seconds squared cancel.

$d=(2820 \ m)+ \frac{1}{2} (-10 \ m * 144 )$

$d=(2820 \ m)+ \frac{1}{2} (-1440 \ m)$

Multiply by 1/2 or divide by 2.

$d= 2820 \ m + (-720 \ m)$

Add.

$d= 2100 \ m$

The firework traveled 2100 meters before exploding.