To answer these questions, we need to consider the properties of motion, such as velocity, time, acceleration, and displacement. Let's break it down step by step:
a) To compute the position of the sandbag at 0.250 seconds, we need to determine how far it has fallen during this time.
First, we need to find the initial velocity of the sandbag when it was released. Since the balloon was rising vertically with a constant velocity of magnitude 5 m/s, the sandbag would also have this initial velocity.
The equation for displacement is given by:
s = ut + (1/2)at^2
Where:
s = displacement
u = initial velocity
t = time
a = acceleration
Since the sandbag is in free fall, the acceleration is equal to the acceleration due to gravity (approximately 9.8 m/s^2), but acting downward.
Substituting the values into the equation, we have:
s = 5 m/s * 0.250 s + (1/2) * (-9.8 m/s^2) * (0.250 s)^2
Simplifying the equation:
s = 1.25 m - 0.30625 m
s ≈ 0.94375 m
Therefore, at 0.250 seconds after its release, the sandbag will have fallen approximately 0.944 meters.
b) To determine how many seconds after its release the sandbag will strike the ground, we can use the equation for displacement:
s = ut + (1/2)at^2
In this case, s represents the displacement of the bag when it reaches the ground. Since the ground is 40 meters below the release point (negative displacement), we can set s = -40 m, u = 5 m/s, and a = -9.8 m/s^2.
-40 = 5t + (1/2)(-9.8)t^2
Simplifying the equation and setting it equal to zero:
(1/2)(-9.8)t^2 + 5t - 40 = 0
This is a quadratic equation, which can be solved using various methods (factoring, quadratic formula, etc.). Solving this equation, we find that t ≈ 4.1153 seconds.
So, approximately 4.115 seconds after its release, the sandbag will strike the ground.
c) Yes, free fall is related to inertia, and understanding Newton's laws of motion is helpful to answer this question. Newton's first law states that an object at rest stays at rest, and an object in motion stays in motion with the same velocity unless acted upon by an external force. In free fall, the only external force acting on the sandbag is gravity. So, understanding the principles of Newton's laws helps us determine the motion of the sandbag in free fall.