# Numerical Analysis

#### Onupoma Islam

##### New member
Assuming that drag is proportional to the square of velocity, we can model the velocity of a
falling object like a parachutist with the following differential equation:
𝑑𝑣/𝑑𝑡 = 𝑔 -(𝑐𝑑/𝑚)*𝑣^2
where 𝑣 is velocity (m/s), 𝑡 is time (s), 𝑔 is the acceleration due to gravity (9.81 m/s^2), 𝑐𝑑 is a
second-order drag coefficient (kg/m), and m is mass (kg). Solve for the velocity and distance
fallen by a 90 kg object with a drag coefficient of 0.225 kg/m. if the initial height is 1 km,
determine when it hits the ground. Obtain your solution with
(i) Euler’s method
(ii) The fourth-order RK method

#### Subhotosh Khan

##### Super Moderator
Staff member
Assuming that drag is proportional to the square of velocity, we can model the velocity of a
falling object like a parachutist with the following differential equation:
𝑑𝑣/𝑑𝑡 = 𝑔 -(𝑐𝑑/𝑚)*𝑣^2
where 𝑣 is velocity (m/s), 𝑡 is time (s), 𝑔 is the acceleration due to gravity (9.81 m/s^2), 𝑐𝑑 is a
second-order drag coefficient (kg/m), and m is mass (kg). Solve for the velocity and distance
fallen by a 90 kg object with a drag coefficient of 0.225 kg/m. if the initial height is 1 km,
determine when it hits the ground. Obtain your solution with
(i) Euler’s method
(ii) The fourth-order RK method
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at: