How Does an Exploding Firework Affect Projectile Landing Distance?

• kenau_reveas
In summary, the larger piece of the shell, with a mass of 4/5 m, lands at a distance of (5/4)r from the mortar after exploding at the top of its trajectory, while the smaller piece, with a mass of 1/5 m, lands at a distance of zero from the mortar. The center of mass of the shell continues on its initial trajectory and can be expressed as (5/4)r in terms of the position it would have landed at without the explosion.
kenau_reveas
A mortar fires a shell of mass m at speed v0. The shell explodes at the top of its trajectory (shown by a star in the figure) as designed. However, rather than creating a shower of colored flares, it breaks into just two pieces, a smaller piece of mass 1/5 m and a larger piece of mass 4/5 m. Both pieces land at exactly the same time. The smaller piece lands perilously close to the mortar (at a distance of zero from the mortar). The larger piece lands a distance d from the mortar. If there had been no explosion, the shell would have landed a distance from the mortar. Assume that air resistance and the mass of the shell's explosive charge are negligible.

Find the distance d from the mortar at which the larger piece of the shell lands.

Express d in terms of .

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The center of mass of the shell will continue on the initial trajectory:

cm = ((1/5)m*0 + (4/5)m*d)m

cm = (4/5)d

d = (5/4)cm where cm is the position it owuld have landed at

it says express d in terms of r. is this d is in terms of r?

kenau_reveas said:
it says express d in terms of r. is this d is in terms of r?

if r is the position it would have landed at

What causes a firework to explode?

A firework explodes due to a chemical reaction between the gunpowder and the fuse. When the fuse is lit, it ignites the gunpowder, creating a rapid expansion of gas, which causes the explosion.

How high do fireworks typically go?

The height of a firework varies depending on its size and design. However, most fireworks can reach heights of 100-200 feet.

What makes a firework explode in different colors?

The colors in a firework are created by adding different chemical compounds, called "stars," to the gunpowder mixture. Each compound emits a different color when ignited, resulting in a colorful explosion.

Are fireworks dangerous?

Fireworks can be dangerous if not handled properly. It is essential to follow safety guidelines and use caution when setting off fireworks. Always have a designated adult in charge, and never point fireworks at people or buildings.

What is the history of fireworks?

Fireworks were invented in China over 2,000 years ago. They were originally used for entertainment and to ward off evil spirits. Today, fireworks are used for celebrations and special events all around the world.

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