You throw a glob of putty straight up toward the ceiling, which is 3.60 m above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is 9.50 m/s. (b) How much time from when it leaves your hand does it take the putty to reach the ceiling?

Video transcript

Hello everyone. So this problem a small rock is thrown by you vertically upward with a speed of 10 m per seconds toward the ceiling which is four m above the point where the small rock leaves your hand. How much is the time taken by the small rock to strike the ceiling? So we're given an initial velocity of 10 m for a second. And were also given that the delta H. Or the distance To strike the ceiling is four m. We can start off by writing the kinetic equations. We recall the f is equal to VI plus squared equals V I squared those two A, delta X and delta X is equal to V I. T plus one half a T squared. So we're given a distance which is equal to delta age. We also know V. I. Now since this is a free fall, The acceleration is simply the acceleration due to gravity which is negative 9.81 m/s squared. And we want to find T. So given V I, delta H and G. We can 3rd kinetic equation to solve this problem. So we can rewrite this as delta H is equal to V I T plus one a half A. Or G. Quick Substitution. four m is equal to 10 m/s. T Plus 1/ times sake of 9.8, 1 meters per second squared t squid. Now we realize that this is a quadratic equation. So we could use the quadratic formula to solve this where in this case actually, instead of actually find the root of T Is equal to the opposite of B plus or minus the square roots of B squared minus four A. C over two A. Where this term will be seen, This term would be be and this term iron term next to the T squared would be a. We can make this substitution. We get that negative 10 plus or minus the square root of squared minus four times one half -9.8. 1 times C. Four. All over two times a. Which a is likewise 1/ 9.81. We compute this. We get some positive time 0.546 seconds. We also get some negative time but that simply does not make sense in this context of the problem. So we only take the positive routes Which is 0.546, which is answer choice. A hope this helps have a great day.