How Far Do Ink Droplets Fall in a Printer?

[tnutty]

Homework Statement

Ink droplets in an ink-jet printer are ejected horizontally at 12 and travel a horizontal distance of 1.0 to the paper.

How far do they fall in this interval?

Homework Equations

?

The Attempt at a Solution

so v0 = 12 m/s

x = 1 mm.

??I am not geting the question

 

[needlottahelp]

umm...i think you use
x = (v0) (t) and solve for time

then use the time for one of the kinematics equation as if it were free fall? does that make sense to you?

 

[tnutty]

can you explain what they mean by " How far do they fall in this interval? "

 

[needlottahelp]

i think basically its just asking for the height the ink dropped from the pen onto the paper

 

[tnutty]

so would this be correct :

x = v0 *t.

t = x/v0

= 1mm / 12 m/s

= 0.001m / 12 m/s

t = 8.3 x 10^-5

so using the equation,

Y = Y0 +Vy0*t -1/2 g*t^2

y = 0 + 12(8.3 x 10^-5) - 1/2 (9.8) (8.3 x 10 ^-5)^2

= 10.0 x 10^-4

 

[needlottahelp]

I see no problem with the time. The equation you used was correct too but the problem is that vyo = 0 m/s and not twelve because the angle of elevation from the horizontal is 0 therefore vyo = sin (0 degrees) (12 m/s) = 0 m/s

 

[tnutty]

Are you sure because vy0 ( read as initial velocity of y) ? which i think should be 12

 

[needlottahelp]

well vy0 is the initial velocity in the y-direction. In other words the vertical direction. The ink was ejected horizontally 12 m/s so that's why the vy0 = 0 m/s

 

[tnutty]

x = v0 *t.

t = x/v0

= 1mm / 12 m/s

= 0.001m / 12 m/s

t = 8.3 x 10^-5

so using the equation,

Y = Y0 +Vy0*t -1/2 g*t^2

y = 0 + 0(8.3 x 10^-5) - 1/2 (9.8) (8.3 x 10 ^-5)^2

= -3.40 x 10^-8...

The number should not be negative?

 

[needlottahelp]

Its negative because of the frame of reference. remember displacement is a vector? its only negative because its downward. the opposite would be true
the distance is just 3.40 x 10^-8

 

[tnutty]

so should the answer be the absolute value of the answer.

 

[needlottahelp]

yes I believe so

 

[tnutty]

Thank you for you help. As you can see I am very new to this and also having a hard time grasping the method and concept of solving physics problem. Although I do not know why, because I am relatively good at quantitative work.