Answer:
the magnitude of the angular magnification of the telescope. is 4
Explanation:
Calculate the magnitude of the angular magnification of the telescope.
Given that,
distance = 25cm
focal length from the objective f₀ = 20cm
focal length from eye piece f₁ = 5cm
The angular magnification of the telescope is
![M = \frac{f_0}{f_1}](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7Bf_0%7D%7Bf_1%7D)
Magnification = 20 / 5
magnification = 4
Hence, the magnitude of the angular magnification of the telescope. is 4
Answer:
a) It is moving at
when reaches the ground.
b) It is moving at
when reaches the ground.
Explanation:
Work energy theorem states that the total work on a body is equal its change in kinetic energy, this is:
(1)
with W the total work, Ki the initial kinetic energy and Kf the final kinetic energy. Kinetic energy is defined as:
(2)
with m the mass and v the velocity.
Using (2) on (1):
(3)
In both cases the total work while the objects are in the air is the work gravity field does on them. Work is force times the displacement, so in our case is weight (w=mg) of the object times displacement (d):
(4)
Using (4) on (3):
(5)
That's the equation we're going to use on a) and b).
a) Because the branch started form rest initial velocity (vi) is equal zero, using this and solving (5) for final velocity:
![v_f=\sqrt{\frac{2mgd}{m}}=\sqrt{2gd}=\sqrt{2*9.8*95}](https://tex.z-dn.net/?f=v_f%3D%5Csqrt%7B%5Cfrac%7B2mgd%7D%7Bm%7D%7D%3D%5Csqrt%7B2gd%7D%3D%5Csqrt%7B2%2A9.8%2A95%7D%20)
![v_f=43.15\frac{m}{s^{2}}](https://tex.z-dn.net/?f=%20v_f%3D43.15%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D)
b) In this case the final velocity of the boulder is instantly zero when it reaches its maximum height, another important thing to note is that in this case work is negative because weight is opposing boulder movement, so we should use -mgd:
![-mgd=-\frac{mv_i^2}{2}](https://tex.z-dn.net/?f=%20-mgd%3D-%5Cfrac%7Bmv_i%5E2%7D%7B2%7D%20)
Solving for initial velocity (when the boulder left the volcano):
![v_i=\sqrt{\frac{2mgd}{m}}=\sqrt{2gd}=\sqrt{2*9.8*525}](https://tex.z-dn.net/?f=v_i%3D%5Csqrt%7B%5Cfrac%7B2mgd%7D%7Bm%7D%7D%3D%5Csqrt%7B2gd%7D%3D%5Csqrt%7B2%2A9.8%2A525%7D%20)
![v_i=101.44 \frac{m}{s^{2}}](https://tex.z-dn.net/?f=v_i%3D101.44%20%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20)