A boy standing on a 20m tall bridge sees a motorboat approaching the bridge at a constant speed. When the boat is 2.7 m from the bridge, the boy drops a stone to the water below. If the stone strikes the water 2.5 m in front of the bow of the boat at what speed is the boat traveling?
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+14903 If the stone strikes the water 2.5 m in front of the bow of the boat at what speed is the boat traveling?
Hello Guest!
\(s_{boat}=2.7m-2.5m=0.2m\)
\(t=\dfrac{s_{boat}}{v_{boat}}=\dfrac{0.2m}{v_{boat}}\)
freefall
\(h=\dfrac{g}{2}t^2\\ t=\sqrt{\dfrac{2h}{g}}=\sqrt{\dfrac{2\cdot 20m}{9.81\dfrac{m}{s^2}}}=2.02\ s\)
\(\dfrac{0.2m}{v_{boat}}=2.02\ s\\ v_{boat}= \dfrac{0.2m}{2.02s}\)
\(v_{boat}=0.099m/s\)
The boat travels at a speed of 0.099 m / s.
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