Answer:
Explanation:
The motion of ballistic pendulum is modelled by the appropriate use of the Principle of Energy Conservation:
The final velocity of the system formed by the ballistic pendulum and the bullet is:
Initial velocity of the bullet can be calculated from the expression derived of the Principle of Momentum:
Answer:
The tension is 
Explanation:
From the question we are told that
The total mass is 
The radius is 
The density of air is 
Generally the upward force acting on the balloon is mathematically represented as
=> 
=> 
Here V is the volume of the spherical helium filled balloon which is mathematically represented as
=> 
=> 
So
Answer:
Explanation:
Generally, length of vector means the magnitude of the vector.
So, given a vector
R = a•i + b•j + c•k
Then, it magnitude can be caused using
|R|= √(a²+b²+c²)
So, applying this to each of the vector given.
(a) 2i + 4j + 3k
The length is
L = √(2²+4²+3²)
L = √(4+16+9)
L = √29
L = 5.385 unit
(b) 5i − 2j + k
Note that k means 1k
The length is
L = √(5²+(-2)²+1²)
Note that, -×- = +
L = √(25+4+1)
L = √30
L = 5.477 unit
(c) 2i − k
Note that, since there is no component j implies that j component is 0
L = 2i + 0j - 1k
The length is
L = √(2²+0²+(-1)²)
L = √(4+0+1)
L = √5
L = 2.236 unit
(d) 5i
Same as above no is j-component and k-component
L = 5i + 0j + 0k
The length is
L = √(5²+0²+0²)
L = √(25+0+0)
L = √25
L = 5 unit
(e) 3i − 2j − k
The length is
L = √(3²+(-2)²+(-1)²)
L = √(9+4+1)
L = √14
L = 3.742 unit
(f) i + j + k
The length is
L = √(1²+1²+1²)
L = √(1+1+1)
L = √3
L = 1.7321 unit
Answer: The electromagnetic waves reach Earth, while the mechanical waves do not.
Explanation:
Answer:
There is an arrow up for air resistance and an arrow down for gravity. The arrow up is longer than the arrow down.
Explanation:
The text of the problem says that the skydiver is slowing down: this means that he has an acceleration, which is directed opposite to the motion of the skydiver. Since the motion is downward, the acceleration must be upward.
There are two forces acting on the skydiver: the gravity (downward) and the air resistance (upward). According to Newton's second law:
F=ma
the acceleration has the same direction of the net force, so the net force must also be upward: therefore, the air resistance must be greater than the gravity, so the arrow up for air resistance is longer than the arrow down for gravity.
