Object Dropped From 500m: Solved with Differential Equations

[my-space]

an object is dropped from a height of 500m. when will object reach the ground level and with what speed?

important: the solution must be by: Differential Equations.

 

[Snark1994]

Okay, so what equations has your lecturer given you that might relate to this problem?

 

[my-space]

the Lecturer gave us a question without any equations or laws - just said to me: do it by using law of free fall !

by the way- our subject is MATH

 

[Riemann Metric]

Your best approach is to use acceleration equals 9.81 meters per second per second. From there, you can integrate your equation until you get a velocity equation and finally the displacement equation. All you need to know is acceleration and once you integrate using initial velocity as zero (or v(0)=0), you can set the displacement equation equal to 500. You can also use basic physics kinematic equations to find the time, and then plug in the time to your velocity equation to find the final velocity.

Note: t=time

A(t)=9.81

V(t)=9.81t+C, but we know C=0 because V(0)=0

D=4.9t²