Physics projectile launcher

Question

a) if you decrease the launch speed what hpens to the flight of time?

b) if you place the launcher on a shorter table what would happen to the time of flight

c) if you increase the mass of the projectile and launched it at a the same initial speed, what would happen to the time of flight?

Answer 1

Hi Kyle!

 

Let's see what we can do with these:

 

a)  The amount of time a projectile stays in the air is solely determined by its vertical motion.  If all else is equal between the two launches, and only the initial launched speed is decreased, the initial vertical velocity will be correspondingly decreased.  Think of if you throw an object just vertically straight up into the air.  If you throw it with less initial speed, it doesn't stay in the air as long and comes back to you sooner.  Even if you add horizontal motion, as well as vertical motion, to you projectile, you can look at each direction independently, and the same still holds true.  Therefore, time of flight will be decreased.

 

b)  We need a bit more information to answer this one fully.  It depends on whether or not the projectile is landing on the table, or on some other surface.  If it is landing on the table, the entire flight will rise and fall together with the changing table height, and there will be no difference.

 

If it is landing on the ground below and you make the table shorter, then, in the vertical direction, the projectile will require less distance covered, and smaller overall displacement, to reach the ground, which may suggest why the time of flight would be decreased.

 

If, for some reason, the projectile is landing on a surface *higher* than the level of the table, the opposite would be true.  A shorter table would increase time of flight, because you are increasing the distance that needs to be covered, and the overall vertical displacement that needs to be accomplished, for the projectile to land.

 

c) If you look at all the kinematic (projectile) equations, you can see that the characteristic motion of projectiles depends on five quantities:  displacement, initial velocity, final velocity, acceleration, and time.  Notice that mass does not appear anywhere in there.  Back from the time of Galileo, for example, it was seen that the falling characteristics of objects did not depend on their mass (if things like air resistance could be ignored).  So, if the more massive object is launched with the same speed and direction as the less massive one, its increased mass will make no difference to time of flight.

 

I hope this helps!  Let me know if you have any other questions about this.

Answer 2

a)

 

Decreasing the launch speed will increase flight time because it takes longer to reach its destination.

 

 

b)

 

The size of the table does not affect the time.  Unless you mean the height of the table.

 

 

c)

 

Increasing the mass would increase the time.  This is due to an increase in weight.  Heavier projectiles will take longer to reach its destination than a lighter weight projectile.