# An object is thrown vertically at a height of 7 m at 1 m/s. How long will it take for the object to hit the ground?

Jun 6, 2018

$\text{1.301 s}$

#### Explanation:

Time taken to reach the same height

${t}_{1} = \text{2u"/"g}$

$\textcolor{w h i t e}{{t}_{1}} = {\text{2 × 1 m/s"/"9.8 m/s}}^{2}$

$\textcolor{w h i t e}{{t}_{1}} = 0.2041 \setminus \text{s}$

Velocity when it hits the ground

"v" = sqrt("u"^2 + "2aS")

$\textcolor{w h i t e}{\text{v") = sqrt(("1 m/s")^2 + "(2 × 9.8 m/s"^2 × "7 m)}}$

color(white)("v") = sqrt(138.2)\ "m/s"

color(white)("v") = 11.75\ "m/s"

Further time taken to reach the ground

${t}_{2} = \text{v – u"/"g}$

$\textcolor{w h i t e}{{t}_{2}} = {\text{11.75 m/s – 1 m/s"/"9.8 m/s}}^{2}$

$\textcolor{w h i t e}{{t}_{2}} = 1.097 \setminus \text{s}$

Total time taken

$\text{T" = t_1 + t_2 = 0.2041\ "s" + 1.097\ "s" = "1.3011 s}$