### Physics Problem: Motion with Air Resistance**Problem Statement:**A rock with a mass of 2 kg is thrown upwards with an initial speed of 19 m/s. The air resistance is proportional to the speed of the rock, with a constant of proportionality \( k = \frac{1}{9} \) kg/s.**Goal:**1. Find an expression for the velocity of the stone as a function of time, assuming it is launched at time \( t = 0 \).2. Determine when the stone reaches its maximum height.**Solution Details:**For the velocity function \( v(t) \):\[ v(t) = \frac{19 + 9.81t}{1 - \frac{t}{9}} \]For the time when the stone reaches its maximum height:\[ t = 171 \, \text{s} \]Note: The problem involves analyzing motion with air resistance, which affects the velocity and time to reach the maximum height.

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Description: ### Physics Problem: Motion with Air Resistance**Problem Statement:**A rock with a mass of 2 kg is thrown upwards with an initial speed of 19 m/s. The air resistance is proportional to the speed of the rock, with a constant of proportionality \( k =

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A rock with mass 2 kg is thrown upwards with an initial speed of 19 m/s. Air resistance is to speed, with constant of proportional 1 proportionality kg/s. 9 v(t) Assuming the stone is launched at time t = 0, find an expression for the velocity of the stone as a function of time. t = - k = 171 When does the stone reach its maximum height? 19 + 9.81t 1− t 9 X X S

A rock with mass 2 kg is thrown upwards with an initial speed of 19 m/s. Air resistance is to speed, with constant of proportional 1 proportionality kg/s. 9 v(t) Assuming the stone is launched at time t = 0, find an expression for the velocity of the stone as a function of time. t = - k = 171 When does the stone reach its maximum height? 19 + 9.81t 1− t 9 X X S

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### Physics Problem: Motion with Air Resistance

**Problem Statement:**

A rock with a mass of 2 kg is thrown upwards with an initial speed of 19 m/s. The air resistance is proportional to the speed of the rock, with a constant of proportionality \( k = \frac{1}{9} \) kg/s.

**Goal:**

1. Find an expression for the velocity of the stone as a function of time, assuming it is launched at time \( t = 0 \).

2. Determine when the stone reaches its maximum height.

**Solution Details:**

For the velocity function \( v(t) \):

\[
v(t) = \frac{19 + 9.81t}{1 - \frac{t}{9}}
\]

For the time when the stone reaches its maximum height:

\[
t = 171 \, \text{s}
\]

Note: The problem involves analyzing motion with air resistance, which affects the velocity and time to reach the maximum height.

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