Question

You are on your balcony and notice some bad squirrels digging in your garden directly below. You start tossing your pistachios at them to get them out of your yard. If the height of your guard rail is 43 inches above the deck, which is at a standard height of 10 feet above the ground, and you toss the pistachios straight down with a speed of 7.4 m/s, then how long does it take for the pistachio to reach the ground?

Answer 1

0.43 s

Step-by-step explanation:

We have the following parameters:

Initial velocity, u = 7.4 m/s

Acceleration of gravity, g = 9.8
`m/s^2`

Distance, s = 43 in + 10 ft = 1.092 m + 3.048 m = 4.14 m

Time, t = ?

Using the equation of motion
`s=ut +(1)/(2)gt^2`, we have

`4.14 = 7.4t + 0.5*9.8t^2`

`4.9t^2 + 7.4t - 4.14 =0`

Using the quadratic formula
`(-b\pm√(b^2-4ac))/(2a)` where a = 4.9, b = 7.4 and c = - 4.14, and solving for the positive value of t only, we have

`t = 0.43` s