Answer:
It will be 66.7 m
Step-by-step explanation:
The jet-ski's velocity relative to the shore is the vector sum of its velocity in still water and the velocity of the current. Since the jet-ski is pointing upstream, the velocity of the current is opposite to the direction of travel of the jet-ski. Therefore, the jet-ski's velocity relative to the shore is:
V_shore = V_still - V_current
V_shore = 40 m/s - 10 m/s = 30 m/s
Distance downstream:
The jet-ski will be carried downstream by the current while it is crossing the river. Therefore, it will be further downstream when it reaches the other side. The distance downstream that the jet-ski will be is equal to the velocity of the current multiplied by the time it takes to cross the river.
Distance downstream = V_current * Time
To find the time it takes to cross the river, we can use the following equation:
Time = Distance / Velocity
Time = 200 m / 30 m/s = 6.67 s
Therefore, the distance downstream that the jet-ski will be when it reaches the other side is:
Distance downstream = 10 m/s * 6.67 s = 66.7 m
Time to reach the other side:
It will take less time for the jet-ski to reach the other side if it points upstream. This is because the current will be pushing the jet-ski in the direction of travel.
To see this mathematically, we can use the following equation for the time it takes to cross the river:
Time = Distance / Velocity
If the jet-ski is pointing upstream, the velocity will be the vector sum of its velocity in still water and the velocity of the current. Since the velocity of the current is opposite to the direction of travel of the jet-ski, the velocity will be smaller than if the jet-ski were pointing downstream. Therefore, the time it takes to cross the river will be shorter.
Conclusion:
The jet-ski's velocity relative to the shore is 30 m/s. It will be 66.7 m downstream when it reaches the other side. It will take less time to reach the other side if it points upstream.