Answer:
The decelerating force is 
Solution:
As per the question:
Frontal Area, A = 
Speed of the spaceship, v = 
Mass density of dust, 
Now, to calculate the average decelerating force exerted by the particle:
(1)
Volume, 
Thus substituting the value of volume, V in eqn (1):
where
A = Area
v = velocity
t = time
(2)
From Newton's second law of motion:
Thus differentiating w.r.t time 't':
where
= average decelerating force of the particle
Now, substituting suitable values in the above eqn:
The kinetic energy of any moving object is
(1/2) (mass) (speed²) .
For the object you described, that's
(1/2) (100 kg) (12.5 m/s)²
= (50 kg) (156.25 m²/s²)
= 7,812.5 joules
______________________________
Your attachment is way out of focus, and impossible to read.
The pressure needed in PSI = Pounds of force needed divided by the cylinder Area
The Cylinder rod Area is 21.19 sq inches
Thus, the pressure= 6800/21.19
= 320.91 PSI
From the conservation of linear momentum of closed system,
Initial momentum = final momentum
Mass of the student, M = 59 kg
Mass of the laser boat, m = 42 kg
Initial speed of student + laser boat, u =0
Final speed of laser boat, v = 1.5 m/s
Final speed of the student = V
(M+m) u =M V +m v
0 = (59 kg) V + (42 kg) (1.5m/s)
V = - 1.06 m/s
Thus, the speed of the student is 1.06 m/s in the opposite direction of the motion of boat.
