King Kong is going to fall three hundred and eighty meters and he starts with a speed of zero meters per second and his acceleration is nine point eight meters per second squared and we’ll choose down to be the positive direction. For part a the time it takes, ‘d’ equals one half ‘a’ times ‘t’ squared and we’ll solve for ‘t’ by multiplying both sides by two and dividing by ‘a’ giving us ‘t2’ equals two ‘d’ divide by ‘a’ and we square root both sides to solve for ‘t’ which is square root two ‘d’ over ‘a’ which means its the square root of two times three hundred and eighty meters over nine point eight meters per second squared which is eight point eight zero six which in two significant figures is eight point eight seconds. It takes him eight point eight seconds to fall off the Empire State Building.
In part b in calculating his final speed I’m choosing to do it this way because this formula doesn’t use the number we’ve calculated, there's some risk that this calculated number could be a mistake and in which case our answer in part be would be wrong if we used it so instead I’m using the formula that involves only the original data. The initial speed is zero and we’ll solve for ‘vf’ which is the square root of two ’a’ times ‘d’ that is the square root of two times nine point eight meters per second squared times three hundred and eighty meters which gives eighty six meters per second as his speed just before he hits the ground.