(b) If a flea can jump straight up to a height of 0.440 m, How long is it in the air?

Video transcript

Hello everyone. So in this problem if a juggler throws a bowling pin vertically upwards to reach a maximum height of 10m then what is its time of flight? So we can begin by drawing the bowling pin, terrible drawing but it'll do it will reach some maximum height max. We want to find the total time. We recall that from the starting point to h max It's 1/2 the total time. And from h max To the starting point is also 1/2 the total time at h max. There is no velocity. You can write the kinetic equations. We recall from this chapter as V F equals V I plus 80. The second one which is B of squared equals V I squared plus two A delta X. And the 3rd 1 delta X is equal to V I T plus one A half A T squared. Now we're given height Aah Max which is equal to m. And we know from these kinda Matic equations that the only equations that involve some distance is equation to an equation three. To make this problem simpler, we don't want to solve for any other extra velocities. We can make the distinction that this zero velocity is V. I. And we can note that it travels from this H max to h equals zero as the final So delta H which is just a F minus H I. In this case would be 0 -10 which is equal to negative 10 m. And in this second phase The time would be 1/2 the total time. And we also recall that the acceleration would just be acceleration due to gravity, which is negative 9.81 m/s square. So we have everything we need to set up this third equation, we could rewrite it as delta H is equal to V I T plus one a half G. T. Sweat. We know that the eye is equal to zero so this term cancels. We want to make this substitution. The time for this second phase Is equal to 1/2 the total time. So we get that delta H is equal to one half G. Total time square. Now we can solve for this total time. Yet two Delta H over G Is equal to 1/4. The total time, swear and finally get an expression for the total time, Which is eight Delta H over G square. Now we can make the substitution. We have delta H and we have G Delta H as we found is negative 10 m. N. G is simply the acceleration due to gravity is 9.81 years for second square And finally we get that the total time is equal to 2.86 seconds. Just answer choice B Hope this helps have a great day