A balloonist, riding in the basket of a hot air balloon that is rising vertically with a constant velocity of 9.5 m/s, releases a sandbag when the balloon is 44.3 m above the ground. Neglecting air resistance, what is the bag's speed when it hits the ground? Assume g = 9.80 m/s2.
Set up the formula,
4.9t^2 +9.5 -44.3 use the quadratic formula to get 2.19 for t.
44.3 = 1/2(9.5 +Vf)2.19
= 30.96 m/s
To determine the speed of the sandbag when it hits the ground, we can use the equations of motion.
First, let's calculate the time it takes for the sandbag to reach the ground. We can use the equation:
h = 0.5 * g * t^2
Where:
h = height (44.3 m)
g = acceleration due to gravity (9.80 m/s^2)
t = time
Rearranging the equation to solve for t:
t^2 = (2 * h) / g
t^2 = (2 * 44.3) / 9.80
t^2 ≈ 9.08
Taking the square root of both sides:
t ≈ √9.08
t ≈ 3.01 s
The time it takes for the sandbag to reach the ground is approximately 3.01 seconds.
Next, we can calculate the speed of the sandbag when it hits the ground using the equation:
v = g * t
Where:
v = final velocity (speed)
g = acceleration due to gravity (9.80 m/s^2)
t = time (3.01 s)
Substituting the values:
v = 9.80 * 3.01
v ≈ 29.48 m/s
Therefore, the sandbag's speed when it hits the ground is approximately 29.48 m/s.
To find the speed of the sandbag when it hits the ground, we can use the equations of motion under constant acceleration. Since the balloon is rising vertically with a constant velocity, the acceleration is equal to the acceleration due to gravity (g).
We are given:
Initial velocity (u) = 0 m/s (since the sandbag is released from rest)
Acceleration (a) = 9.80 m/s² (acceleration due to gravity)
Final velocity (v) = ? (the speed at which the sandbag hits the ground)
Distance (s) = 44.3 m (the height of the balloon when the sandbag is released)
Using the equation:
v^2 = u^2 + 2as
We plug in the values:
v^2 = 0^2 + 2 * 9.80 * 44.3
Simplifying:
v^2 = 0 + 871.96
v^2 = 871.96
To find v, we take the square root of both sides:
v = √871.96
v ≈ 29.54 m/s
Therefore, the sandbag's speed when it hits the ground is approximately 29.54 m/s.