1. ## Kinematic Challenge Problem.

A meteor strikes the Earth's atmosphere and immediately starts to decelerate. Starting at one second after entering the atmosphere the magnitude deceleration is:

where is a constant and is the time in seconds since the meteor entered the atmosphere. If the initial speed of the meteor, one second after entering the atmosphere, is m/s and the length of the meteor's path from one second after entering the atmosphere to impact is then how long after entering the atmosphere does the meteor impact the ground? The path that the meteor travels can assumed to be a straight
line.

This question is considered a challenge question, however I tried to solve it by integrating to attain the expression for velocity and displacement and using the given time = 1 and the given velocity at t = 1 to solve for the constant C and then used the equation to solve for when the displacement from the earth's surface is 0. Again though, I was unsuccessful, can anyone help me out?

2. Originally Posted by jpatrie
A meteor strikes the Earth's atmosphere and immediately starts to decelerate. Starting at one second after entering the atmosphere the magnitude deceleration is:

where is a constant and is the time in seconds since the meteor entered the atmosphere. If the initial speed of the meteor, one second after entering the atmosphere, is m/s and the length of the meteor's path from one second after entering the atmosphere to impact is then how long after entering the atmosphere does the meteor impact the ground? The path that the meteor travels can assumed to be a straight
line.

This question is considered a challenge question, however I tried to solve it by integrating to attain the expression for velocity and displacement and using the given time = 1 and the given velocity at t = 1 to solve for the constant C and then used the equation to solve for when the displacement from the earth's surface is 0. Again though, I was unsuccessful, can anyone help me out?

I get $t = \frac{L + \sqrt{L^2+k^2}}{k}$