A motorboat whose speed in still water is 2.91 m/s must aim upstream at an angle of 30.0 degrees (with respect to a line perpendicular to the shore) in order to travel directly across the stream.
- What is the speed of the current?
- What is the resultant speed of the boat with respect to the shore?
current=2.91sin30=..
speed of boat across 2.91cos30
UN MUCHACHO QUE PESA 300N ESTA SENTADO
EN UN COLUMBIO CALCULAR LA FUERZA HORIZONTAL QUE ES NECESARIO EJERCER SOBRE EL MUCHACHO Y LA TENSION SOBRE LA CUERDAS QUE SOSTIENE EL COLUMBIO
SI FORMA UN ANGULO DE 30GRADO CON LA VERTICAL
To find the speed of the current, you can use the trigonometric relationship between the boat's speed in still water and its resultant velocity when traveling at an angle upstream.
Let's denote the speed of the current as Vc, and the speed of the boat in still water as Vb. The resultant velocity of the boat with respect to the shore can be calculated using the formula:
Vr = √((Vc * cos(θ))^2 + (Vb + Vc * sin(θ))^2)
Where:
Vr is the resultant velocity of the boat,
Vc is the speed of the current,
Vb is the speed of the boat in still water, and
θ is the angle between the boat's direction and a line perpendicular to the shore.
In this case, Vb is given as 2.91 m/s, and θ is given as 30.0 degrees.
To find the speed of the current, we'll use the fact that when the boat travels directly across the stream, its resultant velocity will be perpendicular to the shore. Thus, the angle between the boat's direction and a line perpendicular to the shore will be 90 degrees.
Now substituting the given values into the equation:
Vr = √((Vc * cos(90))^2 + (2.91 + Vc * sin(90))^2)
Since cos(90) = 0 and sin(90) = 1, we can simplify the equation:
Vr = √((Vc * 0)^2 + (2.91 + Vc * 1)^2)
Vr = √(0 + (2.91 + Vc)^2)
Vr = √((2.91 + Vc)^2)
Vr = 2.91 + Vc
Since the resultant velocity should equal the boat's speed in still water, we have:
Vr = Vb
Thus, we can equate the two equations:
2.91 + Vc = 2.91
Simplifying this equation, we find:
Vc = 0 m/s
Therefore, the speed of the current is 0 m/s. This means there is no current in the stream.
To find the resultant speed of the boat with respect to the shore, we can substitute Vc = 0 m/s into the equation:
Vr = 2.91 + Vc
Vr = 2.91 + 0
Vr = 2.91 m/s
Therefore, the resultant speed of the boat with respect to the shore is 2.91 m/s.