3.1 Is the hot air balloon in free fall? Choose from YES or NO - NSC Physical Sciences - Question 3 - 2021 - Paper 1

To find the speed of the hot air balloon, we use the information that it is moving upward at a constant speed. Since no specific speed is given, we denote the speed as 'v'. Therefore, the speed of the hot air balloon is: v = constant.

Using the formula for free fall, we can determine the time it takes stone A to hit the ground. We start from the height of 200 m:

h = rac{1}{2}gt^2

i.e. 200 = rac{1}{2} imes 9.81 imes t^2 Solving for t, we get:

$t^2 = \frac{400}{9.81} \approx 40.8$

Thus, $t \approx 6.39 \text{ seconds}$.

Stone B is dropped 5 seconds after stone A. In those 5 seconds, the hot air balloon continues to rise at speed 'v' (which we cannot quantify). The additional distance covered by the balloon when A strikes the ground can be calculated using:

$d = vt$

Where:

• t is the time taken by stone A to fall (6.39 seconds),
• v is the speed of the balloon.

Thus the total distance from the height of the balloon at that moment:

$ext{final height} = 200 + vt - 200$

This gives:

$d = v(6.39 + 5)$

At this moment, stone A has just struck the ground and the calculated distance will depend on the unknown value 'v'.

To draw the position-time graphs:

1. Graph for the hot-air balloon: Start at 200 m and draw a line increasing at a constant slope, indicating constant speed upward.
2. Graph for stone A: Begin at 200 m and draw a downward parabola starting from that point to 0 m, showing acceleration due to gravity.

Ensure both axes are clearly labeled and the balloon graph is identified as 'BALLOON' and stone A as 'A'.