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roblemSet9: Problem 5 points) A motor boat is traveling southwest at 8 meters per second in a river whose current is 6 meters per second east. What is the resultant speed of the motorboat? 5.667252333 meters per second If the width of the river is 110 meters, how long would it take the boat to cross from one bank to the other? ◻ seconds What distance downstream does the motorboat reach the opposite shore? (NOTE: A negative answer is used to indicate that the boat lands upstream ◻ meters

roblemSet99: Problem 55\newlinepoints)\newlineA motor boat is traveling southwest at 88 meters per second in a river whose current is 66 meters per second east.\newlineWhat is the resultant speed of the motorboat? 55.667252333667252333 meters per second\newlineIf the width of the river is 110110 meters, how long would it take the boat to cross from one bank to the other? □ \square seconds\newlineWhat distance downstream does the motorboat reach the opposite shore? (NOTE: A negative answer is used to indicate that the boat lands upstream □ \square meters

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Q. roblemSet99: Problem 55\newlinepoints)\newlineA motor boat is traveling southwest at 88 meters per second in a river whose current is 66 meters per second east.\newlineWhat is the resultant speed of the motorboat? 55.667252333667252333 meters per second\newlineIf the width of the river is 110110 meters, how long would it take the boat to cross from one bank to the other? □ \square seconds\newlineWhat distance downstream does the motorboat reach the opposite shore? (NOTE: A negative answer is used to indicate that the boat lands upstream □ \square meters
  1. Calculate Resultant Speed: Calculate the resultant speed of the motorboat using the Pythagorean theorem since the river current and the boat's direction form a right angle.\newlineResultant speed = boat speed2+current speed2\sqrt{\text{boat speed}^2 + \text{current speed}^2}\newlineResultant speed = 82+62\sqrt{8^2 + 6^2}\newlineResultant speed = 64+36\sqrt{64 + 36}\newlineResultant speed = 100\sqrt{100}\newlineResultant speed = 1010 meters per second
  2. Find Time to Cross River: Find the time it takes to cross the river by dividing the width of the river by the resultant speed.\newlineTime =WidthResultant speed= \frac{\text{Width}}{\text{Resultant speed}}\newlineTime =110 meters10 meters per second= \frac{110 \, \text{meters}}{10 \, \text{meters per second}}\newlineTime =11 seconds= 11 \, \text{seconds}
  3. Calculate Downstream Distance: Calculate the distance downstream the motorboat will reach using the current speed and the time calculated.\newlineDownstream distance = Current speed ×\times Time\newlineDownstream distance = 66 meters per second ×\times 1111 seconds\newlineDownstream distance = 6666 meters

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