To solve this problem we will use the linear motion kinematic equations, for which the change of speed squared with the acceleration and the change of position. The acceleration in this case will be the same given by gravity, so our values would be given as,

Through the aforementioned formula we will have to

The particulate part of the rest, so the final speed would be



Now from Newton's second law we know that

Here,
m = mass
a = acceleration, which can also be written as a function of velocity and time, then

Replacing we have that,


Therefore the force that the water exert on the man is 1386.62
The magnitude of vector b is 8.58 Unit.
Since both the vectors a and b are perpendicular to each other, so we can apply the Pythagoras theorem to calculate the magnitude of the vector b.
Applying the Pythagoras theorem
(a-b)^2=a^2+b^2
15^2=12.3^2-b^2
b=8.58 unit
Therefor the magnitude of the vector b is 8.58 unit.
Answer:
A) 138.8g
B)73.97 cm/s
Explanation:
K = 15.5 Kn/m
A = 7 cm
N = 37 oscillations
tn = 20 seconds
A) In harmonic motion, we know that;
ω² = k/m and m = k/ω²
Also, angular frequency (ω) = 2π/T
Now, T is the time it takes to complete one oscillation.
So from the question, we can calculate T as;
T = 22/37.
Thus ;
ω = 2π/(22/37) = 10.5672
So,mass of ball (m) = k/ω² = 15.5/10.5672² = 0.1388kg or 138.8g
B) In simple harmonic motion, velocity is given as;
v(t) = vmax Sin (ωt + Φ)
It is from the derivative of;
v(t) = -Aω Sin (ωt + Φ)
So comparing the two equations of v(t), we can see that ;
vmax = Aω
Vmax = 7 x 10.5672 = 73.97 cm/s
Answer:
f=-1380N
Explanation:
A karate master wants to break a board by hitting the board swiftly with his hand. The master's hand has a mass of 0.30 kg, and as it strikes the board, his hand has a velocity of 23.3 m/s. The master contacts the board for 0.0050 seconds
.the concluding part to the question should be
What is the impact force (impulse) on the board?
solution
from the Newton's second law of motion which states that
the rate of change in momentum is directly proportional to the force applied
f=m(v-u)/t
f=0.3(0-23.3)/0.005
f=-1380N
f=force impact
m=mass of the karates master's hand
t=time for the impact
v=0m/s final velocity
u=initial velocity
Initial speed = 56mph
Final speed = 35mph
Time taken = 6.7seconds...
Converting the time to hour.. Divide by 3600..
= 6.7/3600
=0.00186hour..
Acceleration = v-u/t
a = 35-56/0.00186
a = -11283.6mph²
The negative sign shows that it decelerated...
V² = u²+2as
(35)² = (56)² + 2×-11283.6×s
Where s is the distance covered within that time...
1225 = 3136 - 22567.2s
22567.2s = 3136-1225
22567.2s = 1911
S = 1911/22567.2
S = 0.08468miles...
But at the end of the question we were made to understand that 1miles = 5280ft
Therefore 0.08468miles = (0.08468×5280)ft
= 447. 11feets...
Which is approximately 447ft.....
Hope this helped.... ?