As the ball rolls down the ramp, there are changes in kinetic and potential energy. How much kinetic energy does the
2 answers:
You might be interested in
(a) 12.8 kg m/s
The impulse delivered by the bat on the baseball is equal to the change in momentum of the baseball:
where we have
m = 0.144 kg is the mass of the ball
v = -47 m/s is the final velocity of the ball
u = 42 m/s is the initial velocity of the ball
Substituting into the equation, we find
And since we are interested in the magnitude only,
(b) 2.78 kN
The impulse exerted on the ball is also equal to the product between the average force and the contact time:
where
F is the average force exerted on the ball
is the contact time
Solving the formula for F, we find
(c) The force exerted on the ball is much larger (1988 times more) than the weigth of the ball
The weight of the ball is given by
where
m = 0.144 kg is the mass of the ball
g = 9.8 m/s^2 is the acceleration due to gravity
Solving the equation for W, we find
So as we see, the force exerted on the ball (2783 N) is almost 2000 times larger than the weight of the ball (1.4 N):
Answer:
the time taken by the astronaut to reach safety = 9.8 hr
Explanation:
The equation for intensity can be written as :
where :
Replacing that into the above previous equation; we have:
However ; the force needed to push the astronaut is as follows:
F = ma
where ;
m = mass of the astronaut and a = its acceleration
we as well say;
Replacing P with 1000 W ; m with 80 kg and for c
Then; a =
a =
It is also known that the battery will run for one hour and after which the battery on the laser will run out
Then to determine the change in the position after the first hour ; we have:
= 0.27 m
Furthermore, the final velocity of the astronaut is determined as:
where ;
replacing and a =
; Then:
Also; when he drifted 5.0 m away from the capsule; the distance is far short of the 5 m but he still have 9 hours left of oxygen . In addition to that, he acceleration is also zero and the final velocity remains the same, so:
To find the final distance traveled by the astronaut ;we have:
where;
= the final distance
d = total distance
So;
The time taken to reach the final distance can be calculated as:
where;
= is the time to reach the final distance
Replacing 4.73 for and
m/s for
We knew the laser was operated for 1 hour; thus the total time taken by the astronaut to reach the final distance is the sum of the time taken to reach the final distance and the operated time of the laser.
Hence ; the time taken by the astronaut to reach safety = 9.8 hr