A ballon is going upwards with velocity of 12 m/s. It releases a packet when it is at a height of 65m from the ground.time taken to reach the ground=?

sciencesolve | Student

You should use the displacement time equation such that:

`s = ut + (1/2)*g*t^2`

You should consider the given velocity upward direction as opposite to gravity direction, hence, you need to write the displacement time equation such that:

`s = -12t + (1/2)*10*t^2`

Notice that the gravitational acceleration is considered of `10 m/s^2` .

`s = -12t + 5t^2`

Since the problem provides the value of s, hence, you should substitute 65 for s in equation above such that:

`65 = -12t + 5t^2 =gt 5t^2 - 12t - 65 = 0`

You need to use quadratic formula such that:

`t_(1,2) = (12+-sqrt(144+1300))/10`

`t_1 = (12+38)/10 =gt t_1=5`

`t_2 = -26/10 = -2.6`

You need to consider only the positive value, hence t=5s.

Hence, evaluating the time needed for the packet to reach the ground yields t = 5s.