Answer:
51.96 years
2) 30 million of years
Explanation:
First we must know the travel time of the ship seen from the earth. The spaceship travels at half the speed of light, this means that the amount of time the spacecraft must spend to travel the same distance is double compared to the light, that is 60 years.
Now due to the speed of the ship, we must take into account relativistic effects, such as time dilation, this is given by:
Where t is the time measured in the ship, t' is the time measured in the earth, inertially moving with velocity v.
Rewriting for t:
This is the amount of time it would take you reach the Whirlpool galaxy in the spaceship.
2) a light year is a measure of distance, which indicates the kilometers that light travels in a year. Thus, the light emitted by Whirlpool galaxy takes 30 million of years reaches our planet.
Answer:
At low pressure-
At high pressure-
Explanation:
Initial speed,
Final speed,
Net horizontal force due to rolling friction mg where m is mass, g is acceleration due to gravity,
is coefficient of rolling friction
From kinematic relation,
For each tire,
Making the subject
Under low pressure of 40 Psi, d=18 m
Therefore,
At a pressure of 105 Psi, d=93.7
Therefore,
Explanation:
First, we need to determine the distance traveled by the car in the first 30 minutes, .
Notice that the unit measurement for speed, in this case, is km/hr. Thus, a unit conversion of from minutes into hours is required before proceeding with the calculation, as shown below
Now, it is known that the car traveled 40 km for the first 30 minutes. Hence, the remaining distance, , in which the driver reduces the speed to 40km/hr is
.
Subsequently, we would also like to know the time taken for the car to reach its destination, denoted by .
.
Finally, with all the required values at hand, the average speed of the car for the entire trip is calculated as the ratio of the change in distance over the change in time.
Therefore, the average speed of the car is 50 km/hr.
a) 50.8 mm
b) The whole image (1:1)
c) It seems reasonable
Explanation:
a)
To project the image on the film, the distance of the film from the lens must be equal to the distance of the image from the lens. This can be found by using the lens equation:
where
f is the focal length of the lens
p is the distance of the object from the lens
q is the distance of the image from the lens
In this problem:
f = 50.0 mm = 0.050 m is the focal length (positive for a convex lens)
p = 3.00 m is the distance of the person from the lens
Therefore, we can find q:
b)
Here we need to find the height of the image first.
This can be done by using the magnification equation:
where:
y' is the height of the image
y = 1.75 m is the height of the real person
q = 50.8 mm = 0.0508 m is the distance of the image from the lens
p = 3.00 m is the distance of the person from the lens
Solving for y', we find:
(the negative sign means the image is inverted)
Therefore, the size of the image (29.6 mm) is smaller than the size of the film (36.0 mm), so the whole image can fit into the film.
c)
This seems reasonable: in fact, with a 50.0 mm focal length, if we try to take the picture of a person at a distance of 3.00 m, we are able to capture the whole image of the person in the photo.