Free fall velocity and distance

Click For Summary
SUMMARY

The discussion centers on calculating the free fall velocity and distance of a 0.1 kg nut thrown from a 10 m tall tree with an initial upward velocity of 4 m/s and a horizontal velocity of 3 m/s. The time to reach the top of the arc is determined using the equation Vf = Vi + at, yielding 0.41 seconds. The time from the top of the arc to the ground is calculated as 1.9 seconds, leading to a total horizontal distance traveled of 3 times the total time of flight.

PREREQUISITES
  • Understanding of kinematic equations, specifically Vf = Vi + at and Yf = Yi + Vit + 1/2at^2
  • Knowledge of projectile motion concepts, including vertical and horizontal components
  • Familiarity with the effects of gravity on motion, specifically g = 9.8 m/s²
  • Ability to solve quadratic equations and interpret their physical significance
NEXT STEPS
  • Learn how to derive and apply the quadratic formula in kinematic problems
  • Study the principles of projectile motion and its components in detail
  • Explore the concept of average velocity in the context of projectile motion
  • Investigate the effects of air resistance on projectile trajectories
USEFUL FOR

Students studying physics, educators teaching kinematics, and anyone interested in understanding projectile motion and free fall calculations.

  • #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.
 
Physics news on Phys.org
  • #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.
 
  • Like
Likes   Reactions: poh
  • #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
 

Similar threads

Replies
5
Views
1K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 25 ·
Replies
25
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
11
Views
3K
  • · Replies 5 ·
Replies
5
Views
6K
  • · Replies 9 ·
Replies
9
Views
2K