Augustine in septic tank (Alice in Wonderland)

[maxtheminawes]

Homework Statement

Flopping about in pain, Augustine starts rolling across the beach at a constant 1.4m/s. This isn’t Augustine’s day as he now rolls into a hole somebody had just dug for a new septic tank. If it takes him 1.01s to hit the bottom of the hole:
a)How deep is the hole?
b)what is hid acc as he falls?
c)what is his final displacement?

Homework Equations

y=yo+vot+1/2at^2
x=xo+vot+1/2at^2
yo=initial y displacement
vo=initial velocity
xo=initial x displacement

The Attempt at a Solution

a)y=yo+vot+1/2at^2
y=1.4sin270+1/2(-9.8)(1.01^2)
y=-6.4
y=6.4m

b)-9.8m/s^2

c)x=xo+vot+1/2at^2
x=1.4(1.01)
x=1.41m
sqrt of (1.41^2+6.4^2)=6.55m
tan-1(6.4/1.41)=77.58
6.55m @ 77.58degrees

 

[Stonebridge]

a) the vertical falling motion is independent of the horizontal, so there is no need to include the horizontal velocity in this. (Where does the angle 270 come from, by the way?)
The initial vertical velocity is zero in this formula.
b) correct
c) you need to use the correct answer for a) for the vertical displacement. The horizontal displacement is correct.

 

[maxtheminawes]

ok, i redid the problem
a)y=1/2(-9.8)(1.01^2)
y=5m
c)x=1.41
y=5
sqrt of (1.41^2+5^2)=5.2m

is this correct?

 

[Stonebridge]

ok, i redid the problem
a)y=1/2(-9.8)(1.01^2)
y=5m
c)x=1.41
y=5
sqrt of (1.41^2+5^2)=5.2m

is this correct?

Yes that's fine now.

 

[asteriatic]

I would first clarify that this scenario is a hypothetical one and not based on any real-life events. I would also point out that the use of the term "Septic tank" in this context is not scientifically accurate, as a septic tank is a system used for wastewater treatment and not a hole in the ground.

Moving on to the calculations, I would first explain that the given equations are correct for calculating the depth of the hole and the final displacement, assuming that the initial displacement and velocity are both zero. However, I would suggest using the equation y=1/2at^2 instead of y=yo+vot+1/2at^2 as the initial displacement and velocity are both zero in this scenario.

For part (a), the depth of the hole is correctly calculated to be 6.4 meters.

For part (b), the acceleration due to gravity is correctly calculated to be -9.8 m/s^2, indicating that Augustine falls with a constant acceleration towards the bottom of the hole.

For part (c), the final displacement is correctly calculated to be 6.55 meters at an angle of 77.58 degrees. I would also mention that the direction of displacement is not specified in the given scenario, so it is assumed to be in the direction of Augustine's motion (towards the bottom of the hole).

Overall, I would suggest using more realistic and scientifically accurate scenarios for problem-solving exercises. Additionally, I would encourage students to double-check their equations and units to ensure accuracy in their calculations.