(a) The time taken for the projectile to reach the maximum height is 32.65 s.
(b) The horizontal range of the projectile is 9,049.1 m.
The given parameters:
- Initial velocity of the projectile, u = 320 m/s
- Angle of projection, = 30 degrees
The time taken for the projectile to reach the maximum height is calculated as follows;
The horizontal range of the projectile is calculated as follows;
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The Supernova will be observed on Earth 60,000 years from now.
<h3>
What is Supernova?</h3>
- A supernova is a star's tremendous and brilliant explosion. It is referred to as a supernova or a supernovae and is abbreviated as SN or SNe.
- This fleeting astronomical occurrence takes place either when a white dwarf is set off into uncontrolled nuclear fusion or during the latter phases of the development of a big star. The original object, known as the progenitor, either disintegrates completely or falls into a neutron star or black hole.
- Before fading over the course of several weeks or months, the peak optical luminosity of a supernova can be similar to that of an entire galaxy.
- Compared to novae, supernovae are more energetic. Nova, which in Latin means "new," refers to what appears to be a transitory new bright star in astronomy. Supernovae can be distinguished from regular novae by the prefix "super-."
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The isotopes half life is 2 hours
Since given the following :
time = 8 hours × 3600s/hr = 28800 seconds
A₀ = 80 Bq as the first registration of detector counts per second
A = 5 Bq as the registration of detector counts per second eight hours later
Using the formula:
∴ A = A₀ e^-λt
∴ A/A₀ = e^-λt
∴ ln (A/A₀) = -λt
∴ λ = -ln (A/A₀) /t = ln2 / t_{1/2}
∴ t_{1/2} = -ln2 / ln(A/A₀) (t)
∴ t_{1/2} = -ln2 / ln(5/80) (8 hours) = 2 hours
Answer:
Explanation: Two samples of blood that have different masses and temperatures and are mixed, we have to find the final temperature of the mixture. the final temperature can be found using the following formula:
(1) Formula basically tells us that the product of mass and temperature remains constant throughout, so the addition of two products of the two separate blood samples would be equal to the product of final temperature and the total mass of the mixture. Mathematically this means that:
Using (1) and plugging in the corresponding values, we get the answer as follows:
Explanation:
(a)
The initial vertical velocity is 13 m/s. At the maximum height, the vertical velocity is 0 m/s.
v = at + v₀
0 = (-9.8) t + 13
t ≈ 1.33 s
(b)
Immediately prior to the explosion, the ball is at the maximum height. Here, the vertical velocity is 0 m/s, and the horizontal velocity is constant at 25 m/s.
v = √(vx² + vy²)
v = √(25² + 0²)
v = 25 m/s
(c)
Momentum is conserved before and after the explosion.
In the x direction:
m vx = ma vax + mb vbx
m (25) = (⅓ m) (0) + (⅔ m) (vbx)
25m = (⅔ m) (vbx)
25 = ⅔ vbx
vbx = 37.5 m/s
And in the y direction:
m vy = ma vay + mb vby
m (0) = (⅓ m) (0) + (⅔ m) (vby)
0 = (⅔ m) (vby)
vby = 0 m/s
Since the vertical velocity hasn't changed, and since Fragment B lands at the same height it was launched from, it will have a vertical velocity equal in magnitude and opposite in direction as its initial velocity.
vy = -13 m/s
And the horizontal velocity will stay constant.
vx = 37.5 m/s
The velocity vector is (37.5 i - 13 j) m/s. The magnitude is:
v = √(vx² + vy²)
v = √(37.5² + (-13)²)
v ≈ 39.7 m/s
