Answer:
The rocket has to be launched 8 m from the hoop
Explanation:
Let's analyze this problem, the rocket is on a car that moves horizontally, so the rocket also has the same speed as the car; The initial horizontal rocket speed is (v₀ₓ = 3.0 m/s).
On the other hand, when starting the engines we have a vertical force, which creates an acceleration in the vertical axis, let's use Newton's second law to find this vertical acceleration
F -W = m a
a = (F-mg) / m
a = F/m -g
a = 7.0/0.500 - 9.8
a = 4.2 m/s²
We see that we have a positive acceleration and that is what we are going to use in the parabolic motion equations
Let's look for the time it takes for the rocket to reach the height (y = 15m) of the hoop, when the rocket fires its initial vertical velocity is zero (I'm going = 0)
y = 
t + ½ a t²
y = 0 + ½ a t²
t = √ 2y/a
t = √( 2 15 / 4.2)
t = 2.67 s
This time is also the one that takes in the horizontal movement, let's calculate how far it travels
x = v₀ₓ t
x = 3 2.67
x = 8 m
The rocket has to be launched 8 m from the hoop
To calculate the center of gravity, divide total weight distance moment by total mass of the system. Thus, the center of gravity is 13 meter from left-hand side.
Answer:
B. IT should have a very broad focus with many variables.
<h2>
Answer:</h2>
|B| = 47.0 units
<h2>
Explanation:</h2>
The sum of two vectors (A) and (B) gives another vector (A + B). i.e
(A + B) = (A) + (B) ----------------(i)
<em>From the question;</em>
Vector A = 28.0 units in the positive y-direction. This means that the value of the x-component is zero and the value of the y-component is +28
In unit vector notation vector A is given as;
A = 0i + 28.0j
Vector A + B = 19.0 units in the negative y-direction. This means that the value of the x-component is zero and the value of the y-component is -19.0
In unit vector notation, vector A + B is given as;
A + B = 0i - 19.0j
To get the magnitude of vector B, make B the subject of the formula in equation (i) as follows;
(B) = (A + B) - (A) ------------------ (ii)
Substitute the values of the vectors (A) and (A + B) into equation (ii) as follows;
(B) = (0i - 19.0j) - (0i + 28.0j)
(B) = - 19.0j - 28.0j
(B) = - 47.0j
The magnitude of B, |B|, is therefore;
|B| = |-47.0|
|B| = 47.0 units
Answer:
-0.912 m/s
Explanation:
When the package is thrown out, momentum is conserved. The total momentum after is the same as the total momentum before, which is 0, since the boat was initially at rest.
where 
are the mass of the child, the boat and the package, respectively. 
are the velocity of the package and the boat after throwing.
