Physics

(1) Suppose that the total distance is x km, then:
For the first half, time of travelling = (x/2)/40 hours
For the second half, time of travelling = (x/2)/60 hours
So total time used to travel = x/80 + x/120 = x/48 hours
Therefore, average speed = x/(x/48) = 48 km/h
(2) From the relation of energy of a photon E = hf, where h and f are the Planck's constant and frequency respectively, we have:
h = E/f
Therefore, the unit should be:
Joule/Hertz
= Joule second (Js)
(3) A shaving mirror is concave in shape, therefore using the relation:
1/u + 1/v = 1/f
where
u = object distance
v = image distance
f = focal length
From the given, we have:
1/1.52 + 1/0.18 = 1/f
f = 0.161 m
So to have an upright image that is twice the actual size, image distance should be twice the object distance and also it is virtual in nature, i.e.
v = -2u
Applying the equation again:
1/u - 1/2u = 1/0.161
1/2u = 1/0.161
2u = 0.161
u = 0.081 m or 8.1 cm
So he should stand 8.1 cm in front of the mirror.

1. An object covers 1/2 of the distance traveling at 40km/h and the other half at 60km/h. Calculate the average speed of the object to cover the distance.
設全程距離是 d，則全程所需的時間t 是
t = (0.5d / 40) + (0.5d / 60) = (1.5d + 1.0d)/120 = d / 48
所以平均速率(average speed)是
v = d / [d/48] = 48km/h

2. Show that the unit of h (plank’s constant) equals to Joules per second.
利用光子的能量推演
E = hf
h = E / f
E(能量)的單位是 J
f(頻率)的單位是 s-1
所以plank’s constant 的單位是 J s (不是Joules per second.)
h = 6.63x10-34 Js

3. A man standing 1.52m in front of a shaving mirror produces an inverted image 18.0cm in front of it. How close to the mirror should he stand if he wants to form an upright image of his chin that is twice the actual size of his chin?
題目的資料不足不能計算。