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

 

[Nickie]

I would approach this problem by using the principles of differential equations, which are mathematical equations that describe the relationship between the rate of change of a quantity and the quantity itself. In this case, we can use differential equations to determine the position and velocity of the object as it falls from a height of 500m.

To begin, we can define the variables in our equation. Let h(t) represent the height of the object at time t and v(t) represent the velocity of the object at time t. We can also assume that the acceleration due to gravity, g, is constant at 9.8 m/s^2.

Next, we can use the differential equation for position, which states that the rate of change of position is equal to the velocity of the object. This can be written as:

dh/dt = v(t)

Similarly, the differential equation for velocity states that the rate of change of velocity is equal to the acceleration of the object. This can be written as:

dv/dt = g

We can use these two equations to create a system of differential equations that describe the motion of the object as it falls. This system can be solved using techniques such as separation of variables or Euler's method.

Once we have solved the system of differential equations, we can determine the time at which the object reaches the ground level by setting h(t) = 0. This will give us the time, t, at which the object reaches the ground.

To calculate the speed of the object at this time, we can use the equation v(t) = gt, where g is the acceleration due to gravity and t is the time at which the object reaches the ground.

Using this approach, we can accurately determine the time and speed at which the object will reach the ground level after being dropped from a height of 500m. This method allows us to use the principles of differential equations to solve real-world problems, providing a rigorous and scientifically sound solution.