Solving Rectilinear Motion Problem Involving Model Rocket

  • Thread starter Thread starter chukie
  • Start date Start date
  • Tags Tags
    Motion
Click For Summary
SUMMARY

The discussion focuses on solving a rectilinear motion problem involving a model rocket's trajectory defined by the function y=60ln(x+1)-6x, where y represents height in feet and x represents horizontal distance in feet. The rocket's horizontal velocity is given as 50 ft/s when it is 20 feet from the launch site. Participants emphasize the use of the chain rule to determine the vertical velocity (dy/dt) at that specific point, clarifying that the position is expressed as a function of horizontal distance rather than time.

PREREQUISITES
  • Understanding of calculus, specifically the chain rule
  • Familiarity with logarithmic functions
  • Knowledge of rectilinear motion concepts
  • Basic skills in solving differential equations
NEXT STEPS
  • Study the application of the chain rule in related motion problems
  • Explore logarithmic differentiation techniques
  • Learn about the relationship between horizontal and vertical motion in projectile motion
  • Investigate how to derive velocity functions from position functions
USEFUL FOR

Students in calculus, physics enthusiasts, and anyone interested in understanding the dynamics of projectile motion and its mathematical modeling.

chukie
Messages
79
Reaction score
0
Sara launches a model rocket in an open field near her house. Its trajectory is described by the function y=60ln(x+1)-6x for x=[0,36.15] where y is the rocket's height (in feet) above the ground and x is the horizontal distance (in feet) between the launch site and a point directly below the rocket.

Given that the rocket's horizontal velocity (dx/dt) is 50 ft/s when it's directly over a point 20 (horizontal) feet from the launch site, determine the rocket's vertical veloctiy (dy/dt) at that point.

I don't know how to go about solving this question, because normally the position is given as a function of time. Can someone help me? Thanks.
 
Physics news on Phys.org
Chain rule!

dy/dt = ?
find this and do value substitutions
 
rootX said:
Chain rule!

dy/dt = ?
find this and do value substitutions

oh yeah! i was overthinking it way too much. thanks though!
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 24 ·
Replies
24
Views
2K
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 53 ·
2
Replies
53
Views
5K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
6
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K