Question

3. Velocity with Linear Air Drag You are at a park tossing a small ball to a friend. The ball has a mass $m$ and you toss it with an initial $\vec{v}_0$ into the air so that your friend standing some distance away will catch it. The mass experiences a drag force from air that is linear with its velocity. a. Find: the velocity of the ball as a function of time. b. Check the Dimensions: Do the dimensions of your equation balance and make sense? Explain. c. Plot: the components of the ball's velocity a function of time. Do your plots make conceptual sense given the physical situation? Explain. d. Evaluate Special Cases: Does your velocity equation make sense at $t = 0$ and at large $t$. Explain. e. Approximate with a Power Series: Do a power series expansion of the vertical component of the velocity to second order in time. f. Consider a Special Case: Show that if the air drag goes to zero, your expansion gives you the equation for the vertical component of the velocity if there is no air drag.

          3. Velocity with Linear Air Drag You are at a park tossing a small ball to a friend. The ball has
a mass $m$ and you toss it with an initial $\vec{v}_0$ into the air so that your friend standing some
distance away will catch it. The mass experiences a drag force from air that is linear with its
velocity.
a. Find: the velocity of the ball as a function of time.
b. Check the Dimensions: Do the dimensions of your equation balance and make
sense? Explain.
c. Plot: the components of the ball's velocity a function of time. Do your plots make
conceptual sense given the physical situation? Explain.
d. Evaluate Special Cases: Does your velocity equation make sense at $t = 0$ and at
large $t$. Explain.
e. Approximate with a Power Series: Do a power series expansion of the vertical
component of the velocity to second order in time.
f. Consider a Special Case: Show that if the air drag goes to zero, your expansion gives
you the equation for the vertical component of the velocity if there is no air drag.

3. Velocity with Linear Air Drag You are at a park tossing a small ball to a friend. The ball has
a mass m and you toss it with an initial v⃗0 into the air so that your friend standing some
distance away will catch it. The mass experiences a drag force from air that is linear with its
velocity.
a. Find: the velocity of the ball as a function of time.
b. Check the Dimensions: Do the dimensions of your equation balance and make
sense? Explain.
c. Plot: the components of the ball's velocity a function of time. Do your plots make
conceptual sense given the physical situation? Explain.
d. Evaluate Special Cases: Does your velocity equation make sense at t = 0 and at
large t. Explain.
e. Approximate with a Power Series: Do a power series expansion of the vertical
component of the velocity to second order in time.
f. Consider a Special Case: Show that if the air drag goes to zero, your expansion gives
you the equation for the vertical component of the velocity if there is no air drag.

Added by Jennifer D.

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