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.
1) weight of the box: 980 N
The weight of the box is given by:

where m=100.0 kg is the mass of the box, and
is the acceleration due to gravity. Substituting in the formula, we find

2) Normal force: 630 N
The magnitude of the normal force is equal to the component of the weight which is perpendicular to the ramp, which is given by

where W is the weight of the box, calculated in the previous step, and
is the angle of the ramp. Substituting, we find

3) Acceleration: 
The acceleration of the box along the ramp is equal to the component of the acceleration of gravity parallel to the ramp, which is given by

Substituting, we find

Explanation:
It is given that,
Mass of bumper car, m₁ = 202 kg
Initial speed of the bumper car, u₁ = 8.5 m/s
Mass of the other car, m₂ = 355 kg
Initial velocity of the other car is 0 as it at rest, u₂ = 0
Final velocity of the other car after collision, v₂ = 5.8 m/s
Let p₁ is momentum of of 202 kg car, p₁ = m₁v₁
Using the conservation of linear momentum as :


p₁ = m₁v₁ = -342 kg-m/s
So, the momentum of the 202 kg car afterwards is 342 kg-m/s. Hence, this is the required solution.
Since the law of gravitation is an inverse square law if you
quadruple the radius the f will drop by a factor of 16 SO the object would
weigh 200/16 = 12.5N
In other words, as the distance, or radius, quadruples the
weight becomes 1/16 of the original weight. Just plug in 4 for r and when you
square it you get 16. The numerator is 1 so that is how the weight becomes
1/16.
B. velocity at position x, velocity at position x=0, position x, and the original position
In the equation
=
+2 a x (x - x₀)
= velocity at position "x"
= velocity at position "x = 0 "
x = final position
= initial position of the object at the start of the motion