A meteorologist models the height of a hot air balloon launched from the ground. The model assumes the balloon travels vertically upwards and travels 450 metres in the first minute. Due to the decrease in temperature as the balloon rises, the balloon will continually slow down. The model suggests that each minute the balloon will travel only 82% of the distance travelled in the previous minute.
Find how high the balloon will travel in the first 10 minutes after it is launched.
recognition of geometric sequence eg
m
The balloon is required to reach a height of at least 2520 metres. Determine whether it will reach this height.
so the balloon will not reach the required height.
Suggest a limitation of the given model.
horizontal motion not taken into account, rate of cooling will not likely be linear, balloon is considered a point mass / size of balloon not considered, effects of wind/weather unlikely to be consistent, a discrete model has been used, whereas a continuous one may offer greater accuracy
Note: Accept any other sensible answer.