Question

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?

Answer 1

`"1.301 s"`

Explanation:

Time taken to reach the same height

`t_1 = "2u"/"g"`

`color(white)(t_1) = "2 × 1 m/s"/"9.8 m/s"^2`

`color(white)(t_1) = 0.2041\ "s"`

Velocity when it hits the ground

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

`color(white)("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 = "v – u"/"g"`

`color(white)(t_2) = "11.75 m/s – 1 m/s"/"9.8 m/s"^2`

`color(white)(t_2) = 1.097\ "s"`

Total time taken

`"T" = t_1 + t_2 = 0.2041\ "s" + 1.097\ "s" = "1.3011 s"`