help with projectile c/o physical science

Question

I know this is a lot but I need help understanding these questions.

 

 

1. an owner owns a firework display company.  one day the owner and the crew is trying out a new firework.  it shoots in the air to its maximum height in 7 seconds but fails to explode.  how long will the owner and the crew have to get out of the way before the firework hits the ground?

 

I think the answer is 7 or less seconds.

 

 

2.  the crew is finally successful in shooting the firework.  they shoot it to its maximum height in 7 seconds and it explodes sending fragments scattering in horizontal directions all around at a speed of 20 meters per second.  assume the air drag is negligible.

 

A.  at the end of 7 seconds how far in a horizontal direction will the fragments have scattered? (although the fragments scatter in different directions, they all are scattering horizontally).

 

B.  what will be teh acceleration of the fragments as they fall vertically?

 

c.  assuming that they all fall from the same maximum height how long will it take the fragments to  hit the ground?

 

d.  what is the path of the fragments as they fall to the ground?

 

3.  why do the fragments follow this path?

 

 

a big thanks

Answer 1

Dear L, yes indeed, objects that go up will come down. The vertical path of an object can be analyzed separately from the horizontal path using vectors. The object goes up and stops when the deceleration from gravity equals the initial speed,

v = v₀ - at  where a = acceleration due to gravity, 9.8 m/sec²  so in 7 sec the object goes up 9.8 x 7 =68.6 meters and falls the same amount. The time up = the time down so they have 7 sec to get out of the way.

 

The distance traveled up = 1/2 at², or 1/2 x 9.8 x 49 for 240.1 meters.  The acceleration is due to gravity, whether going up or down.

 

As the fragments go horizontally, their speed is independent of gravity but their time in the air is limited by the fall, so they go 20 x 7 meters or 140 meters horizontally. They fall in a parabolic path just like any projectile or a baseball you throw horizontally. As they go horizontal, gravity pulls them down which creates the curved downward path.

 

Dorene O.