# What is the velocity of the ball after H height? Considering wind resistance?

I've been trying to figure out this problem for hours my whole group and most of the class is stumped. We understand that we need to relate the equations of F=ma, Fd = (Cd*p*v^2*A)/2, Fnet=Fd-Fg. No data is given. The answer is a V=____ equation. Even just an answer to #1 would be very helpful! Thanks!

1. Homework Statement

A spherical ball of mass m is dropped from a height H above
the surface of a large water tank. The depth of the water below
is D . The ball hits surface of the water and then continues down
into the water tank, eventually coming to rest at the bottom of the
tank. You should assume that air and water resistance are *not*
negligible in this problem.

1. What is the velocity of the ball when it hits the water?

2. What is the velocity of the ball at the moment it hits the bottom of
the tank?

3. Please draw time-aligned graphs of position, velocity, and acceleration of the ball for its
entire trip from the moment it is dropped until the moment it comes to rest at the bottom of the
tank.

## Homework Equations

F=ma, Fd = (Cd*p*v^2*A)/2, Fnet=Fd-Fg.

## The Attempt at a Solution

All I've got so far is: Fnet = Fg - Fair = mg - kv(t) = ma(t)

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SteamKing
Staff Emeritus
Homework Helper
I've been trying to figure out this problem for hours my whole group and most of the class is stumped. We understand that we need to relate the equations of F=ma, Fd = (Cd*p*v^2*A)/2, Fnet=Fd-Fg. No data is given. The answer is a V=____ equation. Even just an answer to #1 would be very helpful! Thanks!

1. Homework Statement

A spherical ball of mass m is dropped from a height H above
the surface of a large water tank. The depth of the water below
is D . The ball hits surface of the water and then continues down
into the water tank, eventually coming to rest at the bottom of the
tank. You should assume that air and water resistance are *not*
negligible in this problem.

1. What is the velocity of the ball when it hits the water?

2. What is the velocity of the ball at the moment it hits the bottom of
the tank?

3. Please draw time-aligned graphs of position, velocity, and acceleration of the ball for its
entire trip from the moment it is dropped until the moment it comes to rest at the bottom of the
tank.

## Homework Equations

F=ma, Fd = (Cd*p*v^2*A)/2, Fnet=Fd-Fg.

## The Attempt at a Solution

All I've got so far is: Fnet = Fg - Fair = mg - kv(t) = ma(t)
According to the problem statement, the drag force on the ball is proportional to velocity squared, so your equation for Fnet needs correcting.

You won't be able to write your equation for v just by doing algebraic manipulations on the various force quantities. You will have to consult with Mr. Calculus for this problem.