Question

A hot air balloon begins to descend towards the ground from a height of 2250 feet.if it descend at the rate of 150 feet per minute find the height after 12 minutes​

Answer 1

Answer:

450 Feet

Step-by-step explanation:

150 feet per minute therefore after 12 minute the Hight descend would be equal to 150*12 which equals 1800 hence minus 1800 from 2250 which equals 450 feet

Answer 2

The height after 12 minutes is 450 feet.

• A hot air balloon would have risen to a height due to the principle that hot air produced inside the balloon makes it rise as it is hotter compared to the cool air surrounding it.
• This height to which it has risen to would hence be 2250 feet as given. It is said to descend or sink down towards the ground after reaching this height.
• As the hot air balloon uniformly covers some distance per time it is travelling down toward the ground level with constant speed.
• The rate at which it is travelling is given. It is said to travel 150 feet for every minute. So, the distance it travels after 12 minutes of time is to be calculated first.
• This can be done using unitary method wherein similar quantities are equated to compute the value of the unknown quantity.
• The unknown measure is calculated by cross multiplying the known quantities together.
• Here, the unknown measure is distance travelled in 12 minutes. Let this be x feet. Thus, by unitary method we have:

                                                  1 minute=150 feet

                                                  12 minute=x feet

• By cross multiplying we have:

                                                  $x\times1=150\times12$

                                              $\implies x=1800\;feet$

• This is the distance it covers in 12 minutes.
• However, this distance is the distance that the hot air balloon covers from the 2250 feet and not from the ground level.
• Here, the total distance from the ground to which the balloon had risen to is 2250 feet.
• The height is asked to be found which means the distance between the hot air balloon and the ground after the 12 minute time period is asked.
• This height will be given by the distance that the balloon needs to cover before reaching the ground. Hence, the height will be given as the total height minus the the height after 12 minutes.
• The difference between the two distances, that is, the total distance and the distance covered after descending for 12 minutes would give the height.

• Thus, we have:

                                          $Height=2250-1800=450$

• Hence the height is 450 feet which is the height of the balloon from the ground level after descending 150 feet per minute for 12 minutes.

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