The correct answer is letter A. 6 millimeters. <span>If an object 18 millimeters high is placed 12 millimeters from a diverging lens and the image is formed 4 millimeters in front of the lens, the height of the image is 6 millimeters.
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Solution:
18 / x = 12 / 4
12x = 72
x = 6mm
Answer:
distance between the dime and the mirror, u = 0.30 m
Given:
Radius of curvature, r = 0.40 m
magnification, m = - 2 (since,inverted image)
Solution:
Focal length is half the radius of curvature, f = 
f = 
Now,
m = - 
- 2 = -
= 2 (2)
Now, by lens maker formula:
v = 
(3)
From eqn (2):
v = 2u
put v = 2u in eqn (3):
2u =
2 = 
2(u - 0.20) = 0.20
u = 0.30 m
Answer:
105.8 m
46 m/s
Explanation:
From the time the rocket is launched to the time it reaches its maximum height:
v = 0 m/s
a = -10 m/s²
t = 9.2 s / 2 = 4.6 s
Find: Δy and v₀
Δy = vt − ½ at²
Δy = (0 m/s) (4.6 s) − ½ (-10 m/s²) (4.6 s)²
Δy = 105.8 m
v = at + v₀
0 m/s = (-10 m/s²) (4.6 s) + v₀
v₀ = 46 m/s
Let's calculate the average acceleration. It is the rate of changing speeds. Hence, we need to calculate the difference of speeds. 10-6=4 m/s. The rate is now
.
In general, the formula for the mean acceleration between two times 1 and 2 is given by:
where v1 and v2 are the speeds at the respective points and T is the time interval between them.
The kinetic energy of any moving object is
K.E. = (1/2) (mass) (speed)² .
To use this simple formula, the 'mass' has to be in kilograms,
and the 'speed' has to be in meters-per-second.
You can see that we have a slight problem that has to be cleaned up:
The speed in the question is given in "kilometers per hour", but we'll
need it in "meters per second". So let's convert that right now:
(600 km/hour) x (1 hour / 3600 seconds) x (1000 meters / km)
= (600 x 1 x 1000 / 3600) (km-hour-meters / hour-second-km)
= 166.67 meters/second .
Now we're ready to plug numbers into the formula for K.E.
(1/2) (mass) (speed)²
= (1/2) (80,000 kg) (166.67 m/s)²
= (40,000 kg) (27,777.8 m²/s²)
= 1,111,111,111 kg-m²/s²
= 1.1... x 10⁹ Joules (choice D)
