Respuesta :
Answer:
Δx=629.35 m
The pilot release the hay 629.35 m in front of the cattle so that the bales land at the point where the cattle are stranded.
Explanation:
Step 1:
Finding initial velocity components:
Initial velocity=v=75 m/s
α=55
[tex]v_{ox}=vcos\alpha\\v_{ox}=75cos55^o\\v_{ox}=43.018 m/s\\v_{oy}=vsin\alpha\\v_{oy}=75sin55^o\\v_{oy}=61.436 m/s[/tex]
Step 2:
[tex]y_o=150\ m[/tex]
Newton Second Equation:
[tex]y-y_o=v_{oy}t+\frac{1}{2}g t^2[/tex]
g=-9.8 m/s^2 (Downward direction)
[tex]v_{oy}=61.436\ m/s[/tex]
y=0 m
Above equation will become:
-150=(61.436)t-(4.90)t^2
Solving the above quadratic equation we will get:
t=-2.09 sec , t=14.63 sec
t= 14.63 sec
Step 3:
Finding the distance:
Using Again Newton equation of motion in x-direction:
[tex]x-x_o=v_{ox}t+\frac{1}{2}a_{x} t^2[/tex]
Since velocity is constant in x- direction, [tex]a_x[/tex] will be zero.
Above equation will be:
[tex]\Delta x=v_{ox}t[/tex]
Δx=(43.018)(14.63)
Δx=629.35 m
The pilot release the hay 629.35 m in front of the cattle so that the bales land at the point where the cattle are stranded.
The pilot should release the hay at a height of 629.35 m.
Given information,
Initial velocity = 75 m/s
Velocity For x-component,
[tex]\bold {V_0x = Vcos \alpha}\\\\\bold {V_0x = 75 cos 55^o}\\\\\bold {V_0x = 43. 018m/s}[/tex]
Velocity for Y-component
[tex]\bold {V_0y = Vsin \alpha}\\\\\bold {V_0y = 75 sin 55^o}\\\\\bold {V_0y = 61. 43m/s}[/tex]
Using Newton's second equation for y-axis,
[tex]\bold {y-y_0 = V_0t + \dfrac {1}{2} gt^2}[/tex]
Where,
g - gravitational acceleration
put the values in the equation,
[tex]\bold {-150=(61.436)t-(4.90)t^2}[/tex]
Solving this quadratic equation, we get 2 values
t = 14.29 s
To find the distance, use Newton's second equation,
[tex]\bold {x-x_0 = V_0t + \dfrac {1}{2} gt^2}[/tex]
Since acceleration is zero because the velocity is constant in x-axis hence .
So,
[tex]\bold {x-x_0 = V_0_xt }[/tex]
[tex]\bold {x- x_0=(43.018)(14.63)}\\\\\bold {x - x_0=629.35 m}[/tex]
Therefore, the pilot should release the hay at 629.35 m.
To know more about Newton's law, refer to the link:
https://brainly.com/question/3715235
