Booklet 1B - Cosmology (Worked Examples) Flashcards

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1
Q
A
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2
Q

An arrow is fired at 400 ms-1 at 30° to horizontal.

Calculate the horizontal and vertical components of the initial velocity.

A

The horizontal component of the initial velocity is given by:
uh = 400 cos30
= 346 ms-1

The vertical component is given by:
uv = 400 sin30
= 200 ms-1

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3
Q

A projectile has the initial velocity components:
Horizontal: 346 ms-1
Vertical: 200 ms-1

Calculate

(a) the time of flight
(b) the greatest height reached
(c) the horizontal range

A

(a) for the whole flight,
u = 200 ms-1
a = -9.8 ms-2
s = 0 m
(landing at the same height it took off)
t = ?

s = ut + ½at2
0 = 200t + ½ x (-9.8) x t2
200t - 4.9t2 = 0
4.9t = 200
t = 40.8 s

(b) at the greatest height, v = 0 ms-1
v2 = u2 + 2as
02 = 2002 + 2 x (-9.8) x s
s = 2040 m

(c) for horizontal motion,
t = 40.8 s
v = 346 ms-1

s = vt
s = 346 x 40.8
s = 14100 m
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4
Q

A projectile has the initial velocity components:
Horizontal: 346 ms-1
Vertical: 200 ms-1

Calculate the height of the projectile after 5 s.

A
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5
Q

A projectile has the initial velocity components:
Horizontal: 346 ms-1
Vertical: 200 ms-1

Calculate the (resultant) velocity of the projectile after 10 s of flight

A
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6
Q

Consider a folder, of mass 0.3 kg and a pen, of mass 0.05 kg, sitting on a desk, 0.25
m apart. Calculate the magnitude of the gravitational force between the two masses.
Assume they can be approximated to spherical objects.

A
m<sub>1</sub> = 0.3 kg
m<sub>2</sub> = 0.05 kg
r = 0.25 m
G = 6.67 x 10<sup>-11</sup> m3 kg<sup>−1</sup> s<sup>−2</sup>
F = ?
F = Gm<sub>1</sub>m<sub>2</sub> / r<sup>2</sup>
F = 6.67 x 10<sup>-11</sup> x 0.3 x 0.05 / 0.25<sup>2</sup>
F = 1.6 x 10<sup>-11</sup> N
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7
Q

A rocket is travelling past Earth at a constant speed of 2.7 × 108 m s–1.
The pilot measures the journey as taking 240 minutes.
How long did the journey take when measured by an observer on Earth?

A
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8
Q

A spaceship is flying away from Earth towards Proxima Centauri at 0.8c. The distance to
Proxima Centauri is 4.2 ly. What does the pilot of the spaceship see this distance as?

A
v = 0.8c
l = 4.2 ly
l' = ?
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9
Q

A girl tries out an experiment to illustrate the Doppler effect by spinning a battery operated
siren around her head at a constant speed of 5.0 ms-1. The siren emits sound
waves with a frequency of 1200 Hz.
Describe what would be heard by a stationary observer standing a few metres away.

A

An observer a few metres away would hear the siren rise and fall in pitch with each rotation.

vs = 5.0 ms-1
fs = 1200 Hz
v = 340 ms-1 (speed of sound)
fo = ?
As the siren is approaching the observer the frequency would be higher:
𝑓o = 𝑓𝑠 (𝑣/𝑣 − 𝑣𝑠)
𝑓o = 1200 (340/340 − 5)
𝑓o = 1218 𝐻𝑧
As the siren is moving away from the observer the frequency would be lower:
𝑓o = 𝑓𝑠 (𝑣/𝑣 + 𝑣𝑠)
𝑓o = 1200 (340/340 + 5)
𝑓o = 1183 𝐻𝑧

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10
Q

The brightest spectral line for Sodium is measured at 589.0 nm on Earth. When the
spectrum from a distant galaxy is studied the equivalent line is found at 601.2 nm.
Calculate
a) The redshift
b) The speed at which the galaxy is moving away from us.

A
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11
Q

A distant galaxy is found to have a speed of recession of 6.2 × 106 ms-1.

Calculate how far away it is.

A
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