#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.....
More information about text formats
Follow @iMATHalino
MATHalino
#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.....
Add new comment