Answer:
f' = 3665.51 Hz
Explanation:
given,
speed of the hawk = 24.7 m/s
frequency of screech emitted by the hawk = 3400 Hz
speed of sound = 331 m/s
By Doppler's effect
f' is the frequency received by the mouse
v is the speed of the sound
v_s is the speed of the hawk
now,
f' = 1.078 x 3400
f' = 3665.51 Hz
The frequency received by the stationary mouse is equal to 3665.51 Hz
Answer:
w = 0.943 rad / s
Explanation:
For this problem we can use the law of conservation of angular momentum
Starting point. With the mouse in the center
L₀ = I w₀
Where The moment of inertia (I) of a rod that rotates at one end is
I = 1/3 M L²
Final point. When the mouse is at the end of the rod
= I w + m L² w
As the system is formed by the rod and the mouse, the forces during the movement are internal, therefore the angular momentum is conserved
L₀ = L_{f}
I w₀ = (I + m L²) w
w = I / I + m L²) w₀
We substitute the moment of inertia
w = 1/3 M L² / (1/3 M + m) L² w₀
w = 1 / 3M / (M / 3 + m) w₀
We substitute the values
w = 1/3 / (1/3 + 0.02) w₀
w = 0.943 w₀
To finish the calculation the initial angular velocity value is needed, if we assume that this value is w₀ = 1 rad / s
w = 0.943 rad / s
Answer:
13.02 m/s the velocity and 86.92 degrees the direction relative to ground
Explanation:
We need to add velocities in vector addition to find the resultant velocity "" of the balloon (the 13 m/s and the 0.7 m/s).
The velocities are at 90 degrees from each other (one pointing up and the other to the East). Notice from the attached image that the resultant velocity vector (picture in red) is actually the hypotenuse of a right angle triangle.
So we use Pythagoras to find the length (magnitude) of the resultant velocity vector:
we can round the answer to 13.02 m/s
Now we need to find the angle that this new vector makes with the ground by using the definition of tangent of an angle that relates the two quantities that we just added:
So we round it to 86.92 degrees
