Given:
distance from the projector lens to the image, di
projector lens focal length, f
distance from the transparency to the projector lens, do
thin lens equation: 1/f = 1/di + 1/do
do = 4 inches
di = 8 feet
convert feet to inches, for uniformity.
1 foot = 12 inches
8 feet * 12 inches/ft = 96 inches
1/f = 1/96 inches + 1/4 inches
Adding fractions, denominator must be the same.
1/f = (1/96 * 1/1) + (1/4 * 24/24)
1/f = 1/96 + 24/96
1/f = 25/96
to find the value of f, do cross multiplication
1*96 = f * 25
96 = 25f
96/25 = f
3.84 = f
The focal length of the project lens is 3.84 inches
Answer:
the magnitude of the average contact force exerted on the leg is 3466.98 N
Explanation:
Given the data in the question;
Initial velocity of hand v₀ = 5.25 m/s
final velocity of hand v = 0 m/s
time interval t = 2.65 ms = 0.00265 s
mass of hand m = 1.75 kg
We calculate force on the hand F
using equation for impulse in momentum
F × t = m( v - v₀ )
we substitute
F × 0.00265 = 1.75( 0 - 5.25 )
F × 0.00265 = 1.75( - 5.25 )
F × 0.00265 = -9.1875
F = -9.1875 / 0.00265
F = -3466.98 N
Next we determine force on the leg F
Using Newton's third law of motion
for every action, there is an equal opposite reaction;
so, F = - F
we substitute
F = - ( -3466.98 N )
F = 3466.98 N
Therefore, the magnitude of the average contact force exerted on the leg is 3466.98 N
You are in an early universe.
In the study of the evolution of the universe, it has been determined before Plank time (before the big bang and right after it), the early universe had the following characteristics:
- There was only one single force acting over all that existed.
- The early universe was very hot and dense because all matter had contracted before the big bang.
- Space and time were wrapped.
These characteristics match the ones described, based on this, we can conclude you are in an early universe.
Learn more about universe in: brainly.com/question/9724831