(3a) Some boats were traveling up and down a river. A satellite recorded the movements of several boats. A motor boat traveled -3.4 miles per hour for 0.75 hours. How far did it go?

(3b) Some boats were traveling up and down a river. A satellite recorded the movements of several boats. A tugboat traveled -1.5 miles in 0.3 hours. What was its velocity?

3a) 2.55 miles

3b) -5 mi/h

Step-by-step explanation:

3a)

In this problem, we want to know the distance travelled by the boat.

For a boat in uniform motion (=constant speed), the distance travelled can be written as

where:

d is the distance travelled

v is the speed

t is the time

For the motor boat in this problem, we have:

v = 3.4 mi/h (we ignore the negative sign, because it only refers to the direction, but here we are considering the speed, which is a scalar and has no direction)

t = 0.75 h is the time

Therefore, the distance travelled is

3b)

The velocity of an object is the ratio between its displacement (change in position) and time taken.

Since velocity is a vector, it has both a magnitude and a direction: so in this case, we also have to consider the sign when expressing the velocity.

The velocity is given by:

where

d is the displacement

t is the time taken

For the tugboat in this problem,

d = -1.5 mi is the displacement

t = 0.3 h is the time taken

So, its velocity is

And the negative sign indicates that the boat is moving in the negative direction.

what's that

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step-by-step explanation: