You can just use basic
trigonometry to solve for the x & y components.
<span>vector a = 10cos(30) i +
10sin(30) j = <5sqrt(3), 5></span>
vector b is only slightly harder because the angle is relative
to vector a, and not the positive x-axis. Anyway, this just makes vector b with
an angle of 135deg to the positive x-axis.
<span>vector b = 10cos(135) i +
10sin(135) j = <-5sqrt(2), 5sqrt(2)></span>
So
now we can do the questions:
r = a + b
r = <5sqrt(3)-5sqrt(2), 5+5sqrt(2)>
(a)
5sqrt(3)-5sqrt(2)
(b)
5+5sqrt(2)
(c)
|r|
= sqrt( (5sqrt(3)-5sqrt(2))2 + (5+5sqrt(2))2 )
=
12.175
(d)
θ = tan-1 (
(5+5sqrt(2)) / (5sqrt(3)-5sqrt(2)) )
θ
= 82.5deg
<span> </span>
On half life is 5370 years; 6 half lives have passed. You just multiply,
5370*6 = 32,220 years
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:
light rays reflect off an object ,strike the mirror ,and are reflected into your eyes
2,062,305 2,062,305 <span>2,062,305</span>