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GalinKa [24]
2 years ago
10

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 explodi

ng, how far did it go?
Physics
1 answer:
azamat2 years ago
6 0

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 <u>2100 meters</u> before exploding.

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