An animal-rescue plane due east at 50 meters per second drops a bale of hay from an altitude of 62 meters. The acceleration due to gravity is 9.81 meters per second squared. If the bale of hay weighs 191 newtons what is the momentum of the bale the moment it strikes the ground? Answer in units of kilograms times meters per second.
Momentum= mass*vf= weight/g * Vf
but vf^2= 2*g*heigh
To find the momentum of the bale the moment it strikes the ground, we can follow these steps:
Step 1: Calculate the time it takes for the bale to fall from 62 meters.
We can use the equation of motion for free-falling objects:
d = (1/2) * g * t^2,
where
d = distance (62 meters),
g = acceleration due to gravity (9.81 meters per second squared),
t = time.
Plugging in the values, we get:
62 = (1/2) * 9.81 * t^2.
Solving for t^2, we get:
t^2 = (2 * 62) / 9.81,
t^2 = 12.616,
t ≈ √12.616 ≈ 3.55 seconds (rounded to two decimal places).
Step 2: Calculate the final velocity of the bale before it hits the ground.
We can use the equation of motion:
v = g * t,
where
v = final velocity,
g = acceleration due to gravity (9.81 meters per second squared),
t = time (3.55 seconds).
Plugging in the values, we get:
v = 9.81 * 3.55,
v ≈ 34.81 meters per second (rounded to two decimal places).
Step 3: Calculate the momentum of the bale the moment it strikes the ground.
Momentum is defined as the product of mass and velocity. To find the mass of the bale, we need to convert the weight to mass.
We know that weight (W) is related to mass (m) by the formula:
W = m * g,
where
W = weight (191 newtons),
g = acceleration due to gravity (9.81 meters per second squared).
Solving for mass, we get:
m = W / g,
m ≈ 191 / 9.81 ≈ 19.49 kilograms (rounded to two decimal places).
Now, we can find the momentum (p) using the formula:
p = m * v,
where
p = momentum,
m = mass (19.49 kilograms),
v = final velocity (34.81 meters per second).
Plugging in the values, we get:
p = 19.49 * 34.81,
p ≈ 678.43 kilogram·meters per second (rounded to two decimal places).
Therefore, the momentum of the bale the moment it strikes the ground is approximately 678.43 kilogram·meters per second.