Answer: 37.981 m/s
Explanation:
This situation is related to projectile motion or parabolic motion, in which the travel of the ball has two components: <u>x-component</u> and <u>y-component.</u> Being their main equations as follows:
<u>x-component:
</u>
(1)
Where:
is the point where the ball strikes ground horizontally
is the ball's initial speed
because we are told the ball is thrown horizontally
is the time since the ball is thrown until it hits the ground
<u>y-component:
</u>
(2)
Where:
is the initial height of the ball
is the final height of the ball (when it finally hits the ground)
is the acceleration due gravity
Knowing this, let's start by finding
from (2):
<u></u>
(3)
(4)
(5)
(6)
Then, we have to substitute (6) in (1):
(7)
And find
:
(8)
(9)
(10)
On the other hand, since we are dealing with constant acceleration (due gravity) we can use the following equation to find the value of the ball's final velocity
:
(11)
(12)
(13) This is the ball's final velocity, and the negative sign indicates its direction is downwards.
However, we were asked to find the <u>ball's final speed</u>, which is the module of the ball's final vleocity vector. This module is always positive, hence the speed of the ball just before it strikes the ground is 37.981 m/s (positive).
Answer:
v<em>min</em> = 0.23 m/s
Explanation:
The golf ball must travel a distance equal to its diameter in the time between blade arrivals to avoid being hit. If there are 12 blades and 12 blade openings and they have the same width, then each blade or opening is 1/24 of a circle of is 2π/24 = 0.26 radians across.
Therefore, the time between the edge of one blade moving out of the way and the next blade moving in the way is
time = angular distance/angular velocity
⇒ t = 0.26 rad / 1.35 rad/s = 0.194 s
The golf ball must get completely through the blade path in this time, so must move a distance equal to its diameter in 0.194 s, therefore the speed of the golf ball is
v =d/t
⇒ v = 0.045 m / 0.194 s = 0.23 m/s
Your answer would be total number of atoms! This is because when you have these equations which require total number of atoms.
Density is the best property to use, as while multiple different metals could create cubes with the same color, mass, or volume, no different metal could create a cube with the same mass and volume. Density is based on mass and volume, and as a result no two different metals will have the same density.
<span>Data:
mass =
110-g bullet
d = 0.636 m
Force =
13500 + 11000x - 25750x^2, newtons.
a) Work, W
W = ∫( F* )(dx) =∫[13500+ 11000x - 25750x^2] (dx) =
W = 13500x + 5500x^2 - 8583.33 x^3 ] from 0 to 0.636 =
W = 8602.6 joule
b) x= 1.02 m
</span><span><span>W = 13500x + 5500x^2 - 8583.33 x^3 ] from</span> 0 to 1.02
W = 10383.5
c) %
[W in b / W in a] = 10383.5 / 8602.6 = 1.21 => W in b is 21% more than work in a.
</span>