**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

(a) From the given expression v=vie-ct-ct=lnvvic=-1tlnvvic=-121.0 sln5.00 m/s12.0 m/s=4.17×10-2 /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

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