Question

An object is thrown vertically from a height of `5 m` at `8 ms^-1`. How long will it take for the object to hit the ground?

Answer 1

Assuming the object is thrown downward, the time taken will be `0.48 s`.

Explanation:

The question doesn't specify whether the object is thrown upward or downward. I will assume it is thrown downward. This means that the initial velocity, `u=8 ms^-1`, is in the same direction as the acceleration due to gravity, `a=9.8 ms^-2`.

Use the formula `d=ut+1/2at^2`, where `d=5m`

`5 = 8t + 1/2*9.8*t^2 = 8t + 4.9t^2`

Rearranging into standard form for quadratic equations:

`4.9t^2 +8t - 5 = 0`

Use the quadratic formula or your preferred method of solving quadratic equations and take only the positive root:

`t=0.48s`

(If the assumption was that the object was thrown upward instead, the initial velocity and the acceleration would have opposite signs: the initial velocity would be `-8ms^-1`.)