Answer:
dart's speed is 11.77 m/s
Explanation:
given data
mass of the gun m = 355 gram = 0.355 kg
height = 18.3 centimeters = 0.183 m
dart = 57.0 gram = 0.057 kg
to find out
dart's speed
solution
we apply here law of conservation of energy that is express as
mgh = 0.5 × m × v² ...........1
so speed of gun will be here as
V =
..................2
V =
V = 1.89 m/s
and
now we find speed of dart by use law of conservation of momentum that is
M×V = m×v ...............3
so speed of the dart is
v = 
v = 
v = 11.77 m/s
so dart's speed is 11.77 m/s
2<span>cos2(θ)−1 = 0
</span><span>2cos2(θ)=1
</span><span>cos2(θ)=1/2
</span><span>2θ=arc cos1/2
</span><span>2θ=60 degrees
</span><span>θ=30 degrees</span>
1) The average velocity is 
2) The instantaneous velocity is 
Explanation:
1)
The average velocity of an object is given by

where
d is the displacement
t is the time elapsed
In this problem, the position of the particle is given by the function

where t is the time.
The position of the particle at time t = 6 sec is

While the position at time t = 12 sec is

So, the displacement is

And therefore the average velocity is

2)
The instantaneous velocity of a particle is given by the derivative of the position vector.
The position vector is

By differentiating with respect to t, we find the velocity vector:

Therefore, the instantaaneous velocity at any time t can be found by substituting the value of t in this expression.
Learn more about velocity:
brainly.com/question/5248528
#LearnwithBrainly
Answer:37 J
Explanation:
Given
Step :1
Heat added Q=44 J
Work done=-20 J

Step :2
Heat added Q=-61 J
work done 



as the process is cyclic


work done in compression is 37 J
The rock strike the water with the speed of 15.78 m/sec.
The speed by which rock hit the water is calculated by the formula
v=
v=
v=15.78 m/sec
Hence, the rock strike the water with the speed of 15.78 m/sec.