How Do You Calculate the Time a Ball Stays Above a Certain Height?

[lando45]

I have my physics exams on Friday so was just revising some of the stuff I covered earlier in the year. I got this question:

"A ball is thrown vertically upwards with a speed 10ms^-1 from a point 2m above horizontal ground. Calculate the length of time for which the ball is 3m or more above the ground."

I did end up getting the correct answer of 1.83s, but I took an extremely long-winded route. I calculated the total time the ball would be in flight, then subtracted the initial part under 3m and the final part under 3m, which I calculated using the simple equations of motion.

I seem to remember earlier on in the year using a much easier and quicker method to get the answer, but I have forgotten it, and can't seem to find it in my notes. How would you go about solving this question?

 

[teken894]

$$y = y_{0} + v_{y0}t + \frac{1}{2}at^2$$

is the general kinematic equation you want to use,
where in your case:

solve the resulting quadratic equation for t