Question

An object is thrown upward with a velocity of 32 ft/s from a stationary balloon which is 48 ft above the ground. If air resistance is ignored, the total time until the object impacts the ground is _____

Answer 1

`t=2.98s`

Step-by-step explanation:

First, we have to calculate the maximum height reached by the object. We use the equations of uniformly accelerated motion:

`y=y_0+v_0t-(gt_1^2)/(2)`

In order to calculate this, we have to know the time taken by the object to reach the maximum height:

`v_f=v_0-gt_1\\0=32(ft)/(s)-(32.15(ft)/(s^2))t_1\\t_1=(-32(ft)/(s))/(-32.15(ft)/(s^2))\\t_1=0.99s`

Now, we can calculate y:

`y=48ft+(32(ft)/(s))0.99s-((32.15(ft)/(s^2))(0.99s)^2)/(2)\\y=63.93ft`

Now, we calculate the time taken by the object in free fall:

`y=y_0+v_0t+(gt_2^2)/(2)\\y=0ft+0(ft)/(s)t+(gt_2^2)/(2)\\t_2=\sqrt(2y)/(g)\\t_2=\sqrt(2(63.93ft))/(32.15(ft)/(s^2))\\t_2=1.99s`

Finally, adding
`t_1` and
`t_2`, we get the total time until the object impacts the ground:

`t=t_1+t_2\\t=0.99s+1.99s\\t=2.98s`