Kinematic Problem: MJ & SP Meet - Find Distance

Click For Summary
SUMMARY

The problem involves calculating the meeting point of two objects in free fall: MJ, who falls from rest, and SP, who jumps downward with an initial velocity of -45 m/s after 1.5 seconds. The acceleration due to gravity is consistently -9.81 m/s² for both. The correct approach requires setting up separate equations for the positions of MJ and SP, taking into account their respective initial conditions and the time elapsed since MJ started falling. The solution must reflect the continuous acceleration of both objects rather than a static analysis.

PREREQUISITES
  • Understanding of kinematic equations, specifically vf = vi + aΔt and Δγ = viΔt + ½αΔt²
  • Knowledge of free fall motion and gravitational acceleration
  • Ability to set up and solve equations involving multiple variables
  • Familiarity with initial and final velocity concepts in physics
NEXT STEPS
  • Study the derivation and application of kinematic equations in free fall scenarios
  • Learn how to analyze motion with multiple objects using simultaneous equations
  • Explore the concept of relative motion in physics
  • Practice solving problems involving free fall with varying initial velocities
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and motion analysis, as well as educators looking for examples of free fall problems involving multiple objects.

physicsguide
Messages
1
Reaction score
0

Homework Statement


MJ falls from rest from a tall building. 1.5 seconds later SP throws himself downward with an initial velocity of -45 meters per second. Find the distance where they meet.
variables:
α1= -9.81 α2=-9.81
Δγ1 = ? Δγ2=?
Δ†1=? Δ†2=? + 1.5
∨i1=0 ∨i2=-45
∨f1=unknown ∨f2=unknown

Homework Equations


vf=vi+aΔt (distance is absent)
Δγ=viΔt+½αΔt^2 (final velocity is absent)

The Attempt at a Solution


I think I have the problem right. I found the final velocity and distance where MJ would be after the 1.5 seconds. then I used that final velocity as the initial velocity for MJ. and used that distance as MJ's starting distance. then I used true statements to say the accelerations are the same in both equations, the times are the same in both equations (since I changed my initial velocity and distance) and My distance for spiderman - 11.04 (what I got for the initial distance of MJ) equals MJ's distance. then I used Δγ=viΔt+½Δt^2, and set it up as
11.04=vi1Δt1+½αΔt1^2-vi2Δt2+½αΔt2^2. since I knew my times and accelerations were the same, I knew subtracting ½αΔt2^2 from ½αΔt1^2, leaving me with 11.04=Vi1Δt1- Vi2Δt2. I then subtracted the initial velocities because the times are the same. Then I divided 11.04 by what I got. Would this way give me the correct answer?
 
Last edited:
Physics news on Phys.org
Man, I though the problem was talking about Michael Jordan and Scottie Pippen!

You should remember that MJ (Michael Jordan or Mary Jane) are still falling after 1.5 sec (and accelerating, no less), so your static approach to finding the time MJ and SP are at the same distance from the top of the building requires a different approach. Try writing separate equations which describe the position of MJ and SP separately, using the fact that both start from the same point.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 15 ·
Replies
15
Views
4K
Replies
8
Views
6K
  • · Replies 3 ·
Replies
3
Views
15K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 5 ·
Replies
5
Views
1K
Replies
2
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K