Nikki is driving a motorboat across a river that flows at 5 m/s. The motorboat has a speed of 12 m/s in still
water. She heads out from one bank in a direction perpendicular to the current. How far does she travel in 3
minutes?
3 min = 180 seconds
downstream = 5 * 180
across = 12 * 180
hypotenuse = sqrt (across^2 + downstream^2)
Well, Nikki is in for a wild ride! With a current flowing at 5 m/s and her motorboat only going 12 m/s in still water, things might get a little... twisted. But let's crunch some numbers and find out how far she travels in 3 minutes!
Since Nikki is heading perpendicular to the current, we can consider her boat's speed relative to the ground. To do this, we can use the Pythagorean theorem, because we have a right triangle formed by Nikki's boat, the river current, and her actual path across the river.
The velocity of Nikki's boat relative to the ground can be found using the formula: V_relative = sqrt(V_boat^2 + V_river^2)
V_boat = 12 m/s (her boat's speed in still water)
V_river = 5 m/s (the river's current)
Plugging in these values, we get:
V_relative = sqrt(12^2 + 5^2)
V_relative = sqrt(144 + 25)
V_relative = sqrt(169)
V_relative = 13 m/s
So, Nikki's boat has a velocity of 13 m/s relative to the ground.
Now, let's calculate the distance she travels in 3 minutes using the formula: distance = velocity x time
Since distance is in meters and the time is in minutes, let's convert 3 minutes to seconds:
3 minutes = 3 x 60 = 180 seconds
Therefore, the distance Nikki travels is:
distance = V_relative x time
distance = 13 m/s x 180 s
distance = 2340 meters
So, Nikki travels approximately 2340 meters across the river in 3 minutes. Just remember to hold on tight and keep an eye out for any clownfish swimming by!
To find out how far Nikki travels in 3 minutes, we first need to calculate her effective velocity, taking into account the current.
1. Convert 3 minutes to seconds:
3 minutes * 60 seconds/minute = 180 seconds.
2. Let's break down Nikki's velocity into its two components: one perpendicular to the current and one parallel to the current.
Since Nikki is driving perpendicular to the current, the perpendicular component of her velocity will be her speed in still water, which is 12 m/s.
The parallel component of her velocity will be the same as the current's velocity since they are traveling in the same direction, which is 5 m/s.
3. Use the Pythagorean theorem to find the effective velocity:
Effective velocity = square root of (perpendicular velocity^2 + parallel velocity^2).
Effective velocity = square root of (12^2 + 5^2) = square root of (144 + 25) = square root of 169 = 13 m/s.
4. To find the distance Nikki travels in 3 minutes, we can multiply her effective velocity by the time traveled:
Distance = velocity * time.
Distance = 13 m/s * 180 seconds = 2340 meters.
Therefore, Nikki travels 2340 meters in 3 minutes.
To find the distance Nikki travels in 3 minutes, we need to consider her speed relative to the water current.
Let's break down the problem step by step:
1. First, we need to determine the velocity of the motorboat with respect to the current. Since Nikki is heading perpendicularly to the current, we can use Pythagoras' theorem to find the velocity vector magnitude:
velocity with respect to current = √(velocity of motorboat)^2 + (velocity of current)^2
velocity with respect to current = √(12 m/s)^2 + (5 m/s)^2
= √(144 m^2/s^2 + 25 m^2/s^2)
= √(169 m^2/s^2)
= 13 m/s
2. Now that we know the velocity of the motorboat relative to the current, we can calculate the distance traveled in 3 minutes (or 3 * 60 = 180 seconds). Distance is given by the formula:
distance = velocity * time
distance = (13 m/s) * (180 s)
= 2340 meters
Therefore, Nikki travels a distance of 2340 meters in 3 minutes.