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
[tex]d=vt[/tex]
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
[tex]d=(3.4)(0.75)=2.55 mi[/tex]
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:
[tex]v=\frac{d}{t}[/tex]
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
[tex]v=\frac{-1.5}{0.3}=-5 mi/h[/tex]
And the negative sign indicates that the boat is moving in the negative direction.
