An animal-rescue plane flying due east at 36.0 m/s drops a bale of hay from an altitude of h = 69.5 m. If the bale of hay weighs F = 176 N, what is the momentum of the bale the moment before it strikes the ground? Give both magnitude and direction.
helppp!!
4.888888889 east i don't know the magnitude
To find the momentum of the bale of hay just before it strikes the ground, we need to use the equation:
Momentum = Mass × Velocity
First, let's find the mass of the bale of hay using its weight:
Weight = Mass × Gravity
Given that the weight of the bale of hay (F) is 176 N and the acceleration due to gravity (g) is approximately 9.8 m/s², we can rearrange the equation to solve for the mass:
Mass = Weight / Gravity
Mass = 176 N / 9.8 m/s² ≈ 17.959 kg
Now, let's find the final velocity of the bale of hay just before it strikes the ground. Since it is dropped from rest, it will accelerate in the downward direction due to gravity. We can use the equation:
Final Velocity = Initial Velocity + (Acceleration × Time)
In this case, the initial velocity is 0 m/s, the acceleration due to gravity is approximately -9.8 m/s² (negative due to the opposing direction to the positive y-axis), and the time is the time it takes for the bale of hay to fall from the height h.
To find the time, we can use the equation for vertical distance in free fall:
h = (1/2) × Acceleration × Time²
Substituting the given values, we can solve for time:
69.5 m = (1/2) × (-9.8 m/s²) × Time²
Time² = (2 × 69.5 m) / (-9.8 m/s²)
Time² ≈ -14.1633 s²
Since time cannot be negative in this case, we only consider the positive square root:
Time ≈ √14.1633 s ≈ 3.76 s
Now we can find the final velocity:
Final Velocity = 0 m/s + (-9.8 m/s²) × 3.76 s
Final Velocity ≈ -36.848 m/s
Since the animal-rescue plane is flying due east at a velocity of 36.0 m/s and the bale of hay is dropped vertically, the horizontal component of the plane's velocity does not affect the final velocity of the bale of hay in the vertical direction.
Therefore, the magnitude of the momentum just before the bale of hay strikes the ground is:
Momentum = Mass × Velocity
Momentum ≈ 17.959 kg × -36.848 m/s
Momentum ≈ -661.694 kg·m/s
The negative sign indicates that the bale of hay has a downward momentum direction.