March 16, 2017 - 9:02am

#1
Differential Equation: Application of D.E: Newton's Law of Motion

double integration calculator with steps beam stress equations difference between orthocenter and circumcenter trapezoid problem ivory cue ball perimeter of an isosceles triangle formula trigonometric functions formula trig formulas for right triangles length of arc of a circle formula triangle with perpendicular sides pythagorean theorem equation casio fx 115 models trapezoidal pyramid circumscribed circle of a triangle polar moment inertia uv formula of differentiation area of frustum of pyramid shear stress for mild steel rate of change calculus examples calculus disk method casio fx 991 es plus manual pdf area of a scalene triangle formula properties of binomial expansion derivitive of trig functions engineering mechanics by fl singer trigonometric substitution integrals general term geometric sequence truss in engineering mechanics overhanging beam definition equation of deflection rectangle inscribed in a circle formula of arithmetic series volume of hemispherical bowl derivation of cone volume formula for shear force and bending moment double angle formula tan bernoulli's equation problems centroid questions formula of resultant force moment of inertia for a rectangle slant height of pyramid frustum of pyramid formula inverse of trigonometric functions helical spring calculation inertia formulas the sides of an angle inscribed in a circle are double angle formulas spherical triangles shear strength bolts how to solve oblique triangles trigonometry basic formulas pyramid slant height formula trig functions right triangle geometric problems in algebra bernouillis equation definition of right circular cone pascal's triangle and binomial theorem moment of inertia of triangle about centroid cuboid or rectangular prism band pulley moments inertia cone development formula calculation of centroid geometry mensuration 2nd moment of inertia ladder leaning against a wall how to solve binomial expansion problems geometric sequence formula calculator intersection of altitudes of a triangle expand using binomial theorem the sum of an arithmetic sequence sigmoid function derivative cantilever strength conical tank volume calculator

#1.

To get the expression of the velocity of the man-boat system, start by getting the net force...

Net force = $100$ N - $60$ N = $40$ N

Getting the acceleration of the system using Newton's second law of motion:

$$Force = mass \times acceleration$$ $$F = ma$$

Then...

$$a = \frac{F}{m}$$ $$a = \frac{40 \space newtons}{25\space kg + 50 \space kg}$$ $$a = 0.53 \space \frac{m}{s^2}$$

Using the kinematic equation $v_f = v_i+at$, where $v_f$ is the final velocity, $v_i$ is the initial velocity, $a$ is the acceleration and $t$ is time

So...

$$v_f = v_i+at$$

Get the acceleration $a$:

$$a = \frac{v_f-v_i}{t}$$ $$0.53 \space \frac{m}{s^2} = \frac{v_f-0 \space \frac{m}{s}}{t}$$

Then express the final velocity $v_f$ of the boat-man system in terms of time:

$\color {green}{v_f = 0.53t}$

#2

The time needed for the boat-man system to reach $5 \space \frac{m}{s}$ would be...

$$v_f = 0.53t$$ $$5 \space \frac{m}{s} = 0.53t$$ $$\color{green}{t = 9.4 \space seconds}$$

Alternate solutions are highly encouraged.....