Answer:
The length of the rope is 1.005 m.
Explanation:
Given that,
Length of rope = 2.0 m
Angular speed = 0.20 rev/s
Linear speed = 5.0 m/s
Since there are no external torques about the rotation axis
We need to calculate the length of the rope
Using conservation of angular momentum
Put the value into the formula
Hence, The length of the rope is 1.005 m.
Answer: 89.803 ft
Explanation:
The complete question is written below:
An astronaut on the moon throws a baseball upward. The astronaut is 6ft, 6 in. tall and the initial velocity of the ball is 30 ft per second. The height s of the ball in feet is given by the equation,s=-2.7t^2+30t+6.5, where t is the number of seconds after the ball is thrown.
The ball will never reach a height of 100ft. How can this be determined algebraically?
We have the following equation that expresses the height as a function of time:
(1)
Now, if we wan to find the maximum height the baseball reaches and prove it is less than 100 ft, we firstly have to find the time the whole parabolic movement lasts and then find which is the time it takes the baseball to reach its maximum height.
So, if we want to calculate , this is fulfilled when , when the baseball hits the ground:
(2)
This is a quadratic equation of the form , and we have to use the quadratic formula if we want to find :
(3)
Where , ,
Substituting the known values and choosing the positive result of the equation:
(4)
Then we can calculate :
(5)
(6)
Substituting (6) in (1):
(7)
(8) This is the maximum height the baseball reaches, as we can see it is less than 100 ft
-- The acceleration due to gravity is 32.2 ft/sec² . That means that the
speed of a falling object increases by an additional 32.2 ft/sec every second.
-- If dropped from "rest" (zero initial speed), then after falling for 4 seconds,
the object's speed is (4.0) x (32.2) = <em>128.8 ft/sec</em>.
-- 128.8 ft/sec = <em>87.8 miles per hour</em>
Now we can switch over to the metric system, where the acceleration
due to gravity is typically rounded to 9.8 meters/sec² .
-- Distance = (1/2) x (acceleration) x (time)²
D = (1/2) (9.8) x (4)² =<em> 78.4 meters</em>
-- At 32 floors per 100 meters, 78.4 meters = dropped from the <em>25th floor</em>.
The 5 points are certainly appreciated, but I do wish they were Celsius points.
20km/s2
Explanation:
a=(final velocity-initial velocity)/time
final velocity=a * time + initial velocity = 2km/s2 * 4s + 12km/s = 20km/s2
I am not 100% sure but i would say D, since it is a smaller object than the test thus needing a shorter wavelength