Ahot air balloon is launched at kirby park, and it ascends at the rate of 7,200 feet per hour. at the same time, a second hot air balloon is launched at newman park, and it ascends at a rate of 4,000 feet per hour. both of the balloons stop ascending after 30 minutes. kirby park has an altitude of 1,705 ft while newman park has an altitude of 3,940 ft. are the balloons ever at the same height at the same time? explain.

We have to calculate the heights above the sea level of both hot air ballons.

heigh above the sea level (hot air ballon)=altitude of  the place + height ascended.

heigth ascend= speed * time

1)Hot air ballon is launched at Kirby park.
Altitude of Kirby park =1705 ft

Heigh above the sea level=1705 ft + (7200 ft/h)(1/2 h)=1705 ft + 3600 ft=
=5305 ft.

2) Hot air ballon in launched at Newman park.
Altitude of Newman park=3940 ft

Heigh above the sea level=3940 ft + (4000 ft/h)(1/2 h)=3940 ft + 2000 ft=
=5940 ft.

the ballons aren´t ever at the same heigth at the same time, because the Newman  park has an altitude more larger than Kirby park, and the height above the sea level when the hot air ballons have ascended, is more larger at Kirby park than the height above the sea level at Newman park  (heigth of the hot air ballons).

Therefore: the hot air balons are not ever at the same hegith at semae time because:

1)
Altitude at Newman park > altitude at Kirby park  (3940 ft > 1705 ft)
2)
Height above the level sea of the hot air balon at Newman park > heigth avove the level sea of the hot air balon at Kirby park. (5940 ft > 5305 ft).

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