[Video] Q13: H = -16t^2 + vt + k the equation above gives the height h, in feet, of a ball t seconds after it is thrown straight up with an initial speed of v feet per second from a height of k feet. which of the following gives v in terms of h, t, and k ?

Explanation for Question 13 From the Math (Calc) Section on the Official Sat Practice Test 3

Now here in number 13, we're given a function, 2 right? Says H is equal to negative 16 T squared plus V times T 3 plus K. And we're told that H is the height and feet of a 4 ball T seconds. So T is time after it's thrown straight up with an 5 initial speed of V and um, 6 from an initial height of K. And so we're trying to find V in 7 terms of HTN. K. So essentially, 8 we're just going to take this equation that I just read out and 9 we're going to solve for V right. 10 And so if we're going to solve for V, the first thing that we 11 need to do is subtract this K from both sides, 12 so that we get rid of the K U of H vice case. 13 He puts a negative 16 T squared plus B times T. 14 And so we're closer now, right? 15 But that negative 16 T squared is still, 16 um, being added to the VT. 17 And so we can get rid of that by adding 16 T squared to 18 both sides. And that'll give us 16 T squared, 19 plus H minus K is equal to V T. 20 And so the last step here to solve for V is going to be 21 to divide by T that way VCs will cancel and we're left with 16 22 T squared, plus H minus K over T is equal to V. 23 And we see that answer choice with a positive, 24 um, 16 T 25 squared off. So immediately we don't see that answer choice. 26 We have to do a little bit of I'm moving around here. 27 And so we can think about separating what we've written here into two fractions. 28 We can think about writing it as 16, uh, 29 T squared over T plus H minus K over T is 30 equal to B. So we've now split it up, right? 31 And we see that this T or this 16 is T squared, 32 which is really a T times T. 33 And so one of these teas will cancel, which is why our best answer 34 then is going to be a D, right, because if one of those teas 35 cancel, we're left with 16 T plus the fraction H minus K 36 over T. And so the reason D is correct is because they've actually simplified 37 the fraction further, so that one of the teas and 16 T squared will 38 cancel.