COUNT TEM Division PY 333-O: Test 1 1. A small rock is thrown vertically upward
ID: 1580866 • Letter: C
Question
COUNT TEM Division PY 333-O: Test 1 1. A small rock is thrown vertically upward with a speed of 49.0 m/s from the apedoen't hit the building The roc edge of the roof of a 40.0-m-tall building on its way back down and lands on the street below. Ignore air resistance A. What is the maximum height reached by rock? B. What is the speed of the rock just before it hits the street? C. How much time elapses from when the rock is thrown until it hits the street? C. At what time(s) is speed half of its initial speed?Explanation / Answer
We have a huge problem here. You didn't use any units. Are we talking feet or meters? Because we are going to have to use the acceleration of gravity, and if you are talking 49 fps and I use 9.8 m/s^2, the answer is going to be wrong. I'll do this assuming you mean meters, and at least you'll understand how, even if you have to redo it using the correct acceleration.
Let's start with the second problem. First, we want to find how long it takes for the rock to reach the apex of its flight. At that point, v will be 0.
v = v0 + a * t
0 m/s = 49.0 m/s - 9.80 m/s^2 * t
-49 m/s = -9.80 m/s^2 * t
-49 m/s / -9.80 m/s^2 = t
t = 5 s
So it takes 5 s to reach the apex.
And what is the height at the apex?
s = s0 + v0 * t + (1/2)at^2
s = 40.0 m + 49 m/s * 5 s + (1/2) * -9.80 m/s^2 * (5s)^2
s = 40.0 m + 245 m - 122.5 m
s = 162.5 m
Now, how long with it take to fall 162.5 m?
s = s0 + v0 * t + (1/2)at^2
0 m = 162.5 m + 0 m/s * t + (1/2) * -9.80 m/s^2 * t^2
-162.5 m = 0 m - 4.90 m/s^2 * t^2
-162.5 m / -4.90 m/s^2 = t^2
33.163 s^2 = t^2
t = 5.758s
Before we go on, does that make sense? it takes 5 s to go up 162.5 - 40 = 122.5 m and 5.758 s to fall about 3 times that distance? Since gravity accelerates, that's reasonable.
So, the total time is 5 s + 5.758 s = 10.758 s
Now that we know what altitude we start falling from, what is the speed of the rock when it hits the street?
v = v0 * t + (1/2) * at^2
v = 0 m/s * 10.758 s + (1/2) * 9.80 m/s^2 * (10.758 s)^2
v = 567.099 m/s