Respuesta :
The mouse will be 4.61 meters distant horizontally. and the owl won't fall into the nest.
What is velocity?
The change of distance with respect to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.
The given data in the problem is
Diameter of nest,d = 30 cm
The velocity of flying, V = 3.50 m/s toward the east
The angle of flying below the horizontal, Θ = 32°
Position of owl,12.0 m above the middle of the 30 cm-diameter nests, at 4.00 m west.
Height of owl above the ground,h = 12 m
Distance from the west direction, a = 4.00 m
The vertical component of velocity,vₐ
The horizontal component of velocity,vₓ
After covering a vertical distance of 12 m, the vertical component of the mouse's velocity, v, is given by
vₐ-u²=2gh
u = asinΘ
Substitute the above value;
vₐ²- (a sin Θ )² = 2gh
Substitute the given value;
vₐ² - (4 sin 32)² = 2 ×9.81 ×12
vₐ² - (4 × 0.53)² = 235.44
vₐ² - 4.494 = 235.44
vₐ² = 235.44 + 4.494
vₐ² = 239.934
vₐ = 15.49 m/s
The time required to descend the aforementioned 12 meters;
[tex]\rm t = \frac{v_{rel}}{g}[/tex]
t = (vₐ - u )/g
t =( vₐ - a sin Θ )/g
Substitute the given value;
t =(15.49 - 4 ×sin 32°) / 9.81
t= (15.49 - 4 * 0.53) / 9.81
t =(15.49 - 2.12) / 9.81
t = 13.37 / 9.81
t= 1.36 s
Horizontal distance traveled for the given period;
x=uₓ × t
x =a cosΘ × t
Substitute the given value;
x = 4×(cos 32°)×1.36
x= 4×0.848×1.36
x= 4.61 m
Hence, the mouse will be 4.61 meters distant in the horizontal direction. and the owl won't fall into the nest,
To learn more about the velocity, refer to the link: https://brainly.com/question/862972.
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