Free fall velocity and distance

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Homework Help Overview

The problem involves a nut thrown from a height of 10 meters with an initial upward velocity of 4 m/s and an initial horizontal velocity of 3 m/s. The discussion focuses on determining the time to reach the top of its arc, the time from the top of the arc to the ground, and the horizontal distance traveled during the entire motion.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of kinematic equations to find the time to the top of the arc and the time to fall to the ground. There are questions about the definitions of variables such as initial height (Yi) and final height (Yf), as well as the acceleration due to gravity.

Discussion Status

There is ongoing exploration of the equations and their application to the problem. Some participants have provided guidance on defining variables and the importance of considering vertical motion separately from horizontal motion. Multiple interpretations of the time intervals involved are being discussed, with no explicit consensus reached.

Contextual Notes

Participants are navigating through potential confusion regarding the signs of acceleration and the correct application of kinematic equations. There is mention of the need for precision in calculations and the implications of negative time values in the context of the problem.

  • #31
poh said:
Vi = 4m/s I think it was all the time vertical velocity
Yes, it was 4m/s, but it only had that vertical velocity at one moment, the moment when it was thrown.
So the 1.9s was from the throw to landing on the ground. You are asked for the time from the top of the arc to landing on the ground.
 
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  • #32
haruspex said:
Yes, it was 4m/s, but it only had that vertical velocity at one moment, the moment when it was thrown.
So the 1.9s was from the throw to landing on the ground. You are asked for the time from the top of the arc to landing on the ground.
it's take same amount of time to go up as go to down. -1.1s is from ground level so when 1.9s-1.1s its where they meet and point is 0 and the diffrence is time from the top of the arc to ground,
 
  • #33
poh said:
it's take same amount of time to go up as go to down. -1.1s is from ground level so when 1.9s-1.1s its where they meet and point is 0 and the diffrence is time from the top of the arc to ground,
I have read that several times and still cannot decipher it.
There are three points in time:
  1. Nut is thrown; height 10m, vertical speed +4m/s
  2. Nut reaches highest point; vertical speed 0
  3. Nut hits ground; height 0
You found that the time from 1 to 3 is 1.9s, and the time from 1 to 2 is 0.41s. In b), you are asked for the time from 2 to 3.
 
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  • #34
haruspex said:
I have read that several times and still cannot decipher it.
There are three points in time:
  1. Nut is thrown; height 10m, vertical speed +4m/s
  2. Nut reaches highest point; vertical speed 0
  3. Nut hits ground; height 0
You found that the time from 1 to 3 is 1.9s, and the time from 1 to 2 is 0.41s. In b), you are asked for the time from 2 to 3.
I see now Thank you :D
 
  • #35
Alternate method using average velocity with upwards positive so g = -9.8 ms-2 and ground level (h) = -10m from projectile launch position. Doesn't add much to what's been discussed above so perhaps more of a summary.

Initial vertical velocity: $$v_i=4\;ms^{-1}$$
Final vertical velocity: $$v_f=-\sqrt{{v_i}^2+2gh}\; ms^{-1}$$
Average vertical velocity: $$ v_{av}=\frac{v_i+v_f}{2}\; ms^{-1}$$
Time of travel: $$ t = \frac{h} {v_{av}} \;s $$
Horizontal displacement: $$ 3t \;m$$

Hence:

a) -4/g
b) t - (-4/g)
c) 3t
 

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