A sandbag is dropped from a Jules Verne hot air balloon, which is ascending vertically at a constant speed of 6 m/s. If the bag is releasedwith the same upward velocity of 6 m/s when t=0 and hits the ground when t=8 s, determine the speed of the bag as it hits the ground.Use g=9.81 m/s2 in your calculation.Question 11Answera.92.56b.45.65c.52.69d.72.48
Question
A sandbag is dropped from a Jules Verne hot air balloon, which is ascending vertically at a constant speed of 6 m/s. If the bag is releasedwith the same upward velocity of 6 m/s when t=0 and hits the ground when t=8 s, determine the speed of the bag as it hits the ground.Use g=9.81 m/s2 in your calculation.Question 11Answera.92.56b.45.65c.52.69d.72.48
Solution
The speed of the bag as it hits the ground can be calculated using the equation of motion:
v = u + gt
where: v is the final velocity (speed of the bag as it hits the ground), u is the initial velocity (upward velocity of the bag when it was released, which is 6 m/s), g is the acceleration due to gravity (9.81 m/s²), and t is the time (8 seconds).
However, since the bag is moving upwards initially and then downwards due to gravity, we consider g as -9.81 m/s².
So, substituting the given values into the equation:
v = 6 + (-9.81) * 8
v = 6 - 78.48
v = -72.48 m/s
The negative sign indicates that the bag is moving downwards, but since speed is a scalar quantity (it does not have a direction), we take the absolute value. So, the speed of the bag as it hits the ground is 72.48 m/s.
Therefore, the correct answer is d. 72.48.
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