An object is thrown vertically up and attains an upward velocity of 10 m/s when it reaches one fourth of its maximum height above its launch point. What was the initial speed of the object? The acceleration of gravity is 9.8 m/s2. Answer in units of m/s
Use third equation of motion . Find height from there by keeping s= h\4 then use third equation of motion again and find U from there
To find the initial speed of the object, we can use the equations of motion for vertical motion.
First, let's denote the initial speed as 'u' and the final speed (when it reaches one fourth of its maximum height) as 'v'.
The upward velocity at one fourth of the maximum height, v = 10 m/s.
We know that the object is thrown vertically up, which means the final speed v is equal to the opposite of the initial speed u. Hence, v = -u.
Using the equation v^2 = u^2 + 2as, where a is the acceleration due to gravity (9.8 m/s^2) and s is the displacement, which is one fourth of the maximum height.
Rearranging the equation to solve for the initial speed u, we get:
u^2 = v^2 - 2as
Substituting the given values: v = 10 m/s and a = 9.8 m/s^2, and s = one-fourth of the maximum height, we can find the initial speed u.
s = (1/4) * maximum height
Now, we can calculate s:
s = (1/4) * maximum height
s = (1/4) * h
Now, we substitute these values into the equation:
u^2 = v^2 - 2as
u^2 = (10 m/s)^2 - 2 * (9.8 m/s^2) * (1/4) * h
Simplifying, we have:
u^2 = 100 m^2/s^2 - 4.9 m/s^2 * h
Now, we need the relation between the maximum height and the initial speed. At the maximum height, the object's velocity becomes zero. So, we can use the equation:
v^2 = u^2 - 2gh
Rearranging the equation to solve for the maximum height h, we get:
h = (u^2 - v^2) / (2g)
Substituting v = -u:
h = (u^2 - (-u)^2) / (2g)
h = (u^2 - u^2) / (2g)
h = 0 / (2g)
h = 0
We can see that the maximum height is 0, which means the object does not reach any maximum height. Therefore, the object must stop and fall back to the ground before reaching any significant height.
Since the maximum height is 0, we cannot determine the initial speed u using this information.