# An object is thrown vertically from a height of #2 m# at #7 m/s#. How long will it take for the object to hit the ground?

##### 3 Answers

It should take 1.6726 seconds.

#### Explanation:

The problem needs to be broken down into two parts: the time it takes the object to reach the apex of the throw (where v=0) and the time it takes to hit the ground from the apex.

Part 1: Time to apex

Assuming a gravitational constant of

We need to know d for the second part, since the object will have to fall d+2 meters (since the object started 2m up)

For the second part, the object will fall 4.5m, with an initial velocity of 0. Since we're traveling in the same direction as gravity, the constant is now

Finally we add the two times together to get the total time:

#### Explanation:

Apply the equation,

So,if it takes time

Solving it we get,

If thrown vertically up,

If thrown vertically down,

#### Explanation:

Object is thrown vertically up or vertically down?

**Case-1: Object thrown vertically up**

Time taken to reach the initial point will be

#t_1 = (2u)/g = (2 × "7 m/s")/"9.8 m/s"^2 = "1.4 s"#

Velocity when it hits the ground

#v = sqrt(u^2 + 2ad)#

#v = sqrt(("7 m/s")^2 + (2 × "9.8 m/s"^2 × "2 m"))#

#v = "9.4 m/s"#

Further time taken to reach the ground

#t_2 = (v - u)/g = ("9.4 m/s "-" 7 m/s")/"9.8 m/s"^2 = "0.24" s#

Total time taken

**Case-2: Object thrown vertically down**

Velocity when it hits the ground

#v = sqrt(u^2 + 2ad)#

#v = sqrt(("7 m/s")^2 + (2 × "9.8 m/s"^2 × "2 m"))#

#v = "9.4 m/s"#

Time taken to reach the ground

#T = (v - u)/g = ("9.4 m/s "-" 7 m/s")/"9.8 m/s"^2 = color(blue)"0.24 s"#