Respuesta :
Answer:
A. 12 m/s
Explanation:
Let’s remember that the definition of velocity is the variation of position of an object respect with to time. We know that the boy dropped the stone when the boat was 27 meters from the bridge and the stone hit the water 3 meters in front of the boat. So, the Boat must have traveled x=27 m-3m=24 m. The next step is calculating the amount of time that took the boat to make that travel; coincidentally, it is the same time that takes the stone to reach the water.
The equation that describes the motion of the stone is:
y = y_0 + v_0 * t+1/2 * a * t^2
The boy drops the stone from rest, so we can say that v_0=0. We can fixate the reference line on top of the bridge, so y_0=0 as well. The equation will be then:
-19,6 m = -1/2 * 9,8 m/s^2 * t^2
t^2= -(19,6 m)/(-4,9 m/s^2) = 4,012 s^2
t=√(4,012 s^2) = 2,003 s
Knowing the time that takes the stone to reach the water, that is the same that time that the boat uses to travel the 24 meters. The velocity of the boat is:
v = ∆x/∆t = (27 m-3 m)/(2,003 s-0s) = 11,9816 m/s ≈ 12 m/s
Have a nice day! :D
Speed is defined as the rate of change of the distance or the height attained. It is a time-based quantity. The speed of the boat will be 12 m/sec.
What is speed?
Speed is defined as the rate of change of the distance or the height attained. it is a time-based quantity.
it is denoted by u for the initial speed while v for the final speed. its si unit is m/sec.
According to the problem condition, when the boat was 27 meters away from the bridge the boy dropped the stone and the stone hit the water when the 3 meters in front of the boat. So, the Boat must have to travel 3 meters less.
d =27 m-3m=24 m
The amount of time the boat took to make that travel is the same as the time required for a stone to reach the water. The equation that describes the free-fall motion
[tex]\rm y=y_0+v_0t+\frac{1}{2} at^{2}[/tex]
As the body is freely falling so that [tex]\rm v_0=0[/tex]
If the top of the height is the reference plane [tex]\rm y_0=0[/tex]
[tex]\rm 19.6=\frac{1}{2} (9.81)t^{2}[/tex]
[tex]\rm t= \sqrt{4} \;sec\\\\\rm t=2 \;sec[/tex]
The time takes for the stone to reach the water is the same as the time taken by the boat to travel the distance of 24 meters. The velocity of the boat will be;
Mathematically speed is given as,
[tex]\rm v= \frac{dx}{dt} \\\\\rm v= \frac{27-3}{2-0} \\\\\rm v=12\; m/sec[/tex]
Hence the speed of the boat will be 12 m/sec.
To learn more about the speed refer to the link;
https://brainly.com/question/7359669
