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
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
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 ā 9.08
Taking the square root of both sides:
t ā ā9.08
t ā 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 ā 29.48 m/s
Therefore, the sandbag's speed when it hits the ground is approximately 29.48 m/s.
We are given:
Initial velocity (u) = 0 m/s (since the sandbag is released from rest)
Acceleration (a) = 9.80 m/sĀ² (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 = ā871.96
v ā 29.54 m/s
Therefore, the sandbag's speed when it hits the ground is approximately 29.54 m/s.