The first step is to represent the vectors shown in the image in Cartesian coordinates.
For the vector C we have a magnitude of 4.8 and an angle 22 ° with the axis -y (direction j)
To write this vector in Cartesian coordinates we must find its component in x (address i) and in the y axis.
So:
For Vector B we have a magnitude of 5.6 and an angle of 33 with the -x axis (-i direction)
So:
So:
Finally the sum of B + C is made component by component in the following way:
Finally the magnitude of f is:
| F | = 8.04
Answer:
0.71 m/s
Explanation:
We find the time it takes the stone to hit the water.
Using y = ut - 1/2gt² where y = height of bridge, u = initial speed of stone = 0 m/s, g = acceleration due to gravity = -9.8 m/s² (negative since it is directed downwards)and t = time it takes the stone to hit the water surface.
So, substituting the values of the variables into the equation, we have
y = ut - 1/2gt²
82.2 m = (0m/s)t - 1/2( -9.8 m/s²)t²
82.2 m = 0 + (4.9 m/s²)t²
82.2 m = (4.9 m/s²)t²
t² = 82.2 m/4.9 m/s²
t² = 16.78 s²
t = √16.78 s²
t = 4.1 s
This is also the time it takes the raft to move from 5.04 m before the bridge to 2.13 m before the bridge. So, the distance moved by the raft in time t = 4.1 s is 5.04 m - 2.13 m = 2.91 m.
Since speed = distance/time, the raft's speed v = 2.91 m/4.1 s = 0.71 m/s
Wave speed = (wavelength) x (frequency)
Wave speed = (3 m) x (15 Hz)
<em>Wave speed = 45 m/s</em>
