A stone is thrown vertically upward. On its way up it passes point A with speed v, and point B, 12.6 m higher than A, with speed v/2. Calculate the maximum height reached by the stone above point B.
I was told the equation to this was "h=1/2(v2)^2/g."
However, I’m still confused…do I have to solve for v2? And what would g be, in this case?
OHHHH. I thought you typed v2, now I see it at v/2. Big difference.
vfinal=vinitial -g t
v/2 = v-gt
t=v/2g
Now, use that time in the height equation.
12=v*t - 1/2 g t^2
12=v(v/2g) - 1/2g (v/2g)^2
now solve for v. Thence, you know v/2.
vf^2=vi^2 +2gh
g= -9.8 vf=0 vi= v/2 from above
h is the height it goes above B
Now, when I'm solving for time, do I not yet know what v/2 is? Like, it would just be "t = v/2 x -9.8?"
I'm so sorry...this is just not making any sense to me yet.
To solve this problem, you will need to use the equations of motion for an object in freefall. The equation you mentioned, h = (v2)^2/(2g), is one of these equations, where h is the height, v is the velocity, and g is the acceleration due to gravity. Let's go through the steps to solve this problem:
1. To find the maximum height reached by the stone above point B, we need to determine the final velocity of the stone at the highest point of its trajectory. Let's call this final velocity v2.
2. We are given two points where the stone has specific velocities. At point A, the stone has a velocity v, and at point B (12.6 m higher than A), the stone has a velocity v/2.
3. Using the equations of motion, we can set up a system of equations to solve for v2 and the height h. The two equations we will use are:
a. v2 = v - gt (from the equation v = u - gt, where u is the initial velocity and g is the acceleration due to gravity)
b. v/2 = v2 - gt (similar to equation a, but for point B)
4. Solve equations a and b simultaneously to find the value of v2. You can start by rearranging both equations to isolate t:
a. t = (v - v2)/g
b. t = v2/g + (v/2)/g = (3v2 + v)/(2g)
5. Since both equations equal time, we can equate them to solve for v2:
(v - v2)/g = (3v2 + v)/(2g)
6. Simplify and solve for v2:
2(v - v2) = 3v2 + v
2v - 2v2 = 3v2 + v
4v - 2v2 = 3v2 + v
4v = 5v2 + v
3v = 5v2
v2 = 3v/5
7. Now that we know v2, we can calculate the maximum height using the equation you mentioned:
h = (v2)^2/(2g)
8. Since g is the acceleration due to gravity, on Earth it is approximately 9.8 m/s^2. Plug in the values and solve for h:
h = (3v/5)^2/(2 * 9.8)
And there you have it! You can now calculate the maximum height reached by the stone above point B using the given information and the equations of motion.