Respuesta :
Answer:
[tex]v_{boat/obs}=18.0\frac{km}{h}[/tex]
Explanation:
The velocity of an object relative to a system[tex]v_{obj/sys}[/tex], the velocity of that system [tex]v_{sys/obs}[/tex] and the velocity measured by an observer at rest [tex]v_{obj/obs}[/tex] are related by the following equation:
[tex]v_{obj/obs}=v_{obj/sys}+v_{sys/obs}[/tex]
In this case, the object is the boat, the system is the water and we are finding the velocity measured by an observer at rest. So, the formula becomes:
[tex]v_{boat/obs}=v_{boat/water}+v_{water/obs}\\\\v_{boat/obs}=12.0\frac{km}{h} +6.00\frac{km}{h}=18.0\frac{km}{h}[/tex]
In words, the velocity of the boat relative to an observer standing on either bank, is 18.0km/h.
Answer:
The velocity of the boat relative to an observer standing on either bank = (12î + 6j) km/h
In layman terms, the velocity of the boat relative to an observer standing on either bank is 13.42 km/h in the 26.6° North of East direction.
Explanation:
Relative velocity of body A with respect to body B, Vab, is given as Va - Vb.
where Va and Vb are velocities of A and B with respect to an external frame of reference.
That is,
Vab = Va - Vb
For this, question, let the observer be our external frame of reference (very convenient as the observer is stationary and not moving)
Let Vb = velocity of boat with respect to our external frame of reference (the observer/the ground) = ?
Va = velocity of the water of the river with respect to our external frame of reference (the observer/the ground) = 6 km/h east = (6j) km/h
Vba = velocity of the boat relative to the river = 12 km/h north = (12î) km/h
Vba = Vb - Va
12î = Vb - 6j
Vb = (12î + 6j) km/h
Magnitude = √[12² + 6²] = 13.42 km/h
Direction = tan⁻¹ (6/12) = 26.6°
