Answer:
doppler shift's formula for source and receiver moving away from each other:
<em>λ'=λ°√(1+β/1-β)</em>
Explanation:
acceleration of spaceship=α=29.4m/s²
wavelength of sodium lamp=λ°=589nm
as the spaceship is moving away from earth so wavelength of earth should increase w.r.t increasing speed until it vanishes at λ'=700nm
using doppler shift's formula:
<em>λ'=λ°√(1+β/1-β)</em>
putting the values:
700nm=589nm√(1+β/1-β)
after simplifying:
<em>β=0.17</em>
by this we can say that speed at that time is: v=0.17c
to calculate velocity at an acceleration of a=29.4m/s²
we suppose that spaceship started from rest so,
<em>v=v₀+at</em>
where v₀=0
so<em> v=at</em>
as we want to calculate t so:-
<em>t=v/a</em> v=0.17c ,c=3x10⁸ ,a=29.4m/s²
putting values:
=0.17(3x10⁸m/s)/29.4m/s²
<em>t=1.73x10⁶</em>
Answer:
Explanation:
a ) V = 3 cos(0.5t)
differentiating with respect to t
dv /dt = -3 x .5 sin0.5t
= -1.5 sin0.5t.
acceleration = - 1.5 sin 0.5t
when t = 3 s
acceleration = - 1.5 sin 1.5
= - 1.496 ms⁻²
v = 3 cos.5t
b ) dx/dt = 3 cos 0.5 t
dx = 3 cos 0.5 t dt
integrating on both sides
x = 3 sin .5t / .5
x = 6 sin0.5t
At t = 2 s
x = 6 sin 1
x = 5.05 m
The representation of this problem is shown in Figure 1. So our goal is to find the vector

. From the figure we know that:

From geometry, we know that:

Then using
vector decomposition into components:

Therefore:

So if you want to find out <span>
how far are you from your starting point you need to know the magnitude of the vector

, that is:
</span>

Finally, let's find the <span>
compass direction of a line connecting your starting point to your final position. What we are looking for here is an angle that is shown in Figure 2 which is an angle defined with respect to the positive x-axis. Therefore:
</span>
Answer:
10. 36 g ZnCl2
Explanation:
Zn + 2HCl -> ZnCl2 + H2
0.076 mol Zn
1.37 mol HCl
3 mol H2
Limiting reactant: Zn
1 mol Zn -> 1 mol ZnCl2
0.076 mol Zn ->x x= 0.076 mol ZnCl2=10.36 g
Answer:
<u>1.8kJ</u>
Explanation:
Formula :
<u>Energy used = Power x time</u>
<u />
===============================================================
Given :
⇒ Power = 30 W
⇒ Time = 1 minute = 60 seconds
=============================================================
Solving :
⇒ Energy used = 30 W × 60 s
⇒ Energy used = 1,800 J
⇒ Energy used = <u>1.8kJ</u>