Lunar lander velocity before hitting ground

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SUMMARY

The discussion focuses on calculating the velocity of a lunar lander just before it impacts the moon's surface, using the height equation y(t) = b - ct + dt², where b = 770m, c = 62.0m/s, and d = 1.02m/s². Participants suggest using the quadratic formula to find the time of impact and then applying the derivative v(t) = dy/dt to determine the velocity at that moment. The conversation emphasizes the importance of recognizing the relationship between position, velocity, and acceleration in kinematic equations.

PREREQUISITES
  • Understanding of kinematic equations, specifically y(t) = y₀ + v₀t + (1/2)at²
  • Familiarity with calculus concepts, particularly derivatives
  • Knowledge of quadratic equations and their applications
  • Basic physics principles related to motion under gravity
NEXT STEPS
  • Study the application of the quadratic formula in physics problems
  • Learn how to differentiate functions to find velocity from position equations
  • Explore the implications of acceleration in motion equations
  • Investigate real-world applications of kinematic equations in aerospace engineering
USEFUL FOR

Students in physics or engineering courses, educators teaching kinematics, and anyone interested in the dynamics of spacecraft landing scenarios.

Lefty9602
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Homework Statement


A lunar lander is descending toward the moon's surface. Until the lander reaches the surface, its height above the surface of the moon is given by y(t)=b−ct+dt2, where b = 770m is the initial height of the lander above the surface, c = 62.0m/s , and d = 1.02m/s2 .
Part B: What is the velocity of the lunar lander before hitting the ground?

Homework Equations

The Attempt at a Solution


quadratic formula to find x intercepts. I don't know how I'm supposed to get the velocity before it hits the ground that could be at any point.
 
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A matter of finding the pertaining relevant equation!
Do you recognize this y(t)=b − c t + d t2 ? Or do I nudge a bit harder by pointing at ##y(t) =y_0 + v_0t + {1\over 2} a t^2 ## ? What is the corresponding ##v(t) = ... ## equation ?

If all else fails, you can also apply ##v_y = {dy\over dt}## if that's familiar to you
 

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