An object is thrown vertically from a height of #12 m# at # 19 ms^-1#. How long will it take for the object to hit the ground?

Answer 1

Assuming the object was thrown downward, the time taken will be #0.55# #s#.

We are aware of:

#u=19# #ms^-1# #d=12# #m# #a=9.8# #ms^-2# #t=?# #s#

Given that both the initial velocity and the acceleration are pointing downward, we are selecting that direction as the positive direction.

Use #d=ut+1/2at^2#

This one is not so easy to rearrange to have #t# as the subject, so let's just substitute in what we know:

#d=ut+1/2at^2 to 12# #19*t +1/2*9.8*t^2#

Put the quadratic back in standard form:

#4.9t^2+19t-12=0#

Using the quadratic formula or any other method of your choice, solve the quadratic equation; this will yield two roots, but only one of them makes sense:

#t= -4.4# #s# or #t=0.55# #s#

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Answer 2

William Audy

The time it takes for the object to hit the ground is approximately 2.19 seconds.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.