Answer: Both cannonballs will hit the ground at the same time.
Explanation:
Suppose that a given object is on the air. The only force acting on the object (if we ignore air friction and such) will be the gravitational force.
then the acceleration equation is only on the vertical axis, and can be written as:
a(t) = -(9.8 m/s^2)
Now, to get the vertical velocity equation, we need to integrate over time.
v(t) = -(9.8 m/s^2)*t + v0
Where v0 is the initial velocity of the object in the vertical axis.
if the object is dropped (or it only has initial velocity on the horizontal axis) then v0 = 0m/s
and:
v(t) = -(9.8 m/s^2)*t
Now, if two objects are initially at the same height (both cannonballs start 1 m above the ground)
And both objects have the same vertical velocity, we can conclude that both objects will hit the ground at the same time.
You can notice that the fact that one ball is fired horizontally and the other is only dropped does not affect this, because we only analyze the vertical problem, not the horizontal one. (This is something useful to remember, we can separate the vertical and horizontal movement in these type of problems)
To solve this problem it is necessary to apply the concepts related to Kinetic Energy, specifically, since it is a body with angular movement, the kinetic rotational energy. Recall that kinetic energy is defined as the work necessary to accelerate a body of a given mass from rest to the indicated speed.
Mathematically it can be expressed as,
Where
I = Moment of Inertia
Angular velocity
Our values are given as
A revolution is made every 4.4 seconds.
If the angular velocity is equivalent to the displacement over the time it takes to perform it then
Replacing at our previous equation we have,
Therefore the kinetic energy is equal to 
Answer:
11.3 m/s
Explanation:
First, find the time it takes for the first stone to fall 3.2 m.
Given:
Δy = 3.2 m
v₀ = 0 m/s
a = 9.8 m/s²
Find: t
Δy = v₀ t + ½ at²
(3.2 m) = (0 m/s) t + ½ (9.8 m/s²) t²
t = 0.81 s
Next, find the time for the first stone to land.
Given:
Δy = 15 m
v₀ = 0 m/s
a = 9.8 m/s²
Find: t
Δy = v₀ t + ½ at²
(15 m) = (0 m/s) t + ½ (9.8 m/s²) t²
t = 1.75 s
The difference in time is 1.75 s − 0.81 s = 0.94 s. Find the initial velocity needed for the second stone to land after that amount of time.
Given:
Δy = 15 m
a = 9.8 m/s²
t = 0.94 s
Find: v₀
Δy = v₀ t + ½ at²
(15 m) = v₀ (0.94 s) + ½ (9.8 m/s²) (0.94 s)²
v₀ = 11.3 m/s
Answer:
False
Explanation:
As technology advances and new evidence is found which either contradicts or supports accepted scientific principles, the principles are susceptible to change.
