A speedboat is cruising at a speed of 12.0 m/s in still water when it shuts off its engines and coasts to rest. The water exerts drag forces on the speedboat such that its speed during coasting is given by v = v,e-ct, where v is the speed at time t, v; is the initial speed at t = 0, and c is a constant. At a time of t = 21.0 s after the engines are cut, the speed is 5.00 m/s. (a) What is the constant c (ins-1) in the expression? s-1 (b) What is the speed (in m/s) at t = 40.0 s? m/s
A speedboat is cruising at a speed of 12.0 m/s in still water when it shuts off its engines and coasts to rest. The water exerts drag forces on the speedboat such that its speed during coasting is given by v = v,e-ct, where v is the speed at time t, v; is the initial speed at t = 0, and c is a constant. At a time of t = 21.0 s after the engines are cut, the speed is 5.00 m/s. (a) What is the constant c (ins-1) in the expression? s-1 (b) What is the speed (in m/s) at t = 40.0 s? m/s
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![**Problem Statement:**
A speedboat is cruising at a speed of 12.0 m/s in still water when it shuts off its engines and coasts to rest. The water exerts drag forces on the speedboat such that its speed during coasting is given by \( v = v_i e^{-ct} \), where \( v \) is the speed at time \( t \), \( v_i \) is the initial speed at \( t = 0 \), and \( c \) is a constant. At a time of \( t = 21.0 \, \text{s} \) after the engines are cut, the speed is 5.00 m/s.
(a) What is the constant \( c \) (in \( \text{s}^{-1} \)) in the expression?
[ ] \( \text{s}^{-1} \)
(b) What is the speed (in m/s) at \( t = 40.0 \, \text{s} \)?
[ ] m/s](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88df49e2-51fc-468b-a659-a66492008d01%2F33a32f0a-b40c-4810-a48e-4c3fecfd5eee%2Fp589k6_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A speedboat is cruising at a speed of 12.0 m/s in still water when it shuts off its engines and coasts to rest. The water exerts drag forces on the speedboat such that its speed during coasting is given by \( v = v_i e^{-ct} \), where \( v \) is the speed at time \( t \), \( v_i \) is the initial speed at \( t = 0 \), and \( c \) is a constant. At a time of \( t = 21.0 \, \text{s} \) after the engines are cut, the speed is 5.00 m/s.
(a) What is the constant \( c \) (in \( \text{s}^{-1} \)) in the expression?
[ ] \( \text{s}^{-1} \)
(b) What is the speed (in m/s) at \( t = 40.0 \, \text{s} \)?
[ ] m/s
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