Answer:
The angle of projection is 12.26⁰.
Explanation:
Given;
initial position of the dart, h₀ = 1.50 m
height above the ground reached by the dart, h₁ = 1.73 m
maximum height reached by the dart, Hm = h₁ - h₀ = 1.73 m - 1.50 m= 0.23 m
velocity of the dart, u = 10 m/s
The maximum height reached by the projectile is calculated as;
where;
θ is angle of projection
g is acceleration due to gravity = 9.8 m/s²
Therefore, the angle of projection is 12.26⁰.
Answer:
b) Betelgeuse would be times brighter than Sirius
c) Since Betelgeuse brightness from Earth compared to the Sun is the statement saying that it would be like a second Sun is incorrect
Explanation:
The start brightness is related to it luminosity thought the following equation:
(1)
where is the brightness,
is the star luminosity and
, the distance from the star to the point where the brightness is calculated (measured). Thus:
b) and
where
is the Sun luminosity (
) but we don't need to know this value for solving the problem.
is light years.
Finding the ratio between the two brightness we get:
c) we can do the same as in b) but we need to know the distance from the Sun to the Earth, which is . Then
Notice that since the star luminosities are given with respect to the Sun luminosity we don't need to use any value a simple states the Sun luminosity as the unit, i.e 1. From this result, it is clear that when Betelgeuse explodes it won't be like having a second Sun, it brightness will be 5 orders of magnitude smaller that our Sun brightness.