Answer:
Explanation:
Given
mass of steel ball 
initial speed of ball 
Final speed of ball
(in upward direction)
Impulse imparted is given by change in the momentum of object
therefore impulse J is given by




so magnitude of Impulse =4 N-s
Answer:
D. the proper replacement unit for one joule per second
Explanation:
When energy is divided by the time the energy was used we get power



So, the answer is D. the proper replacement unit for one joule per second
Answer:
619.8 N
Explanation:
The tension in the string provides the centripetal force that keeps the rock in circular motion, so we can write:

where
T is the tension
m is the mass of the rock
v is the speed
r is the radius of the circular path
At the beginning,
T = 50.4 N
v = 21.1 m/s
r = 2.51 m
So we can use the equation to find the mass of the rock:

Later, the radius of the string is decreased to
r' = 1.22 m
While the speed is increased to
v' = 51.6 m/s
Substituting these new data into the equation, we find the tension at which the string breaks:

Answer:
f = 6.37 Hz, T = 0.157 s
Explanation:
The expression you have is
y = 5 sin (3x - 40t)
this is the equation of a traveling wave, the general form of the expression is
y = A sin (kx - wt)
where A is the amplitude of the motion, k the wave vector and w the angular velocity
Angle velocity and frequency are related
w = 2π f
f = w / 2π
from the equation w = 40 rad / s
f = 40 / 2π
f = 6.37 Hz
frequency and period are related
f = 1 / T
T = 1 / f
T = 1 / 6.37
T = 0.157 s
Consider the upward direction of motion as positive and downward direction of motion as negative.
a = acceleration due to gravity in downward direction = - 9.8 
v₀ = initial velocity of rock in upward direction = ?
v = final velocity of rock at the highest point = 0 
t = time to reach the maximum height = 4.2 sec
Using the kinematics equation
v = v₀ + a t
inserting the values
0 = v₀ + (- 9.8) (4.2)
v₀ = 41.2 