How much thrust is required to move a boat of 120 kg / 265 pounds to a speed of ....

Question

How much thrust is required to move a boat of 120 kg / 265 pounds to a speed of 10 km / 6 miles per hour in 7 seconds.

I found the following:

• http://en.wikipedia.org/wiki/Thrust-to-weight_ratio
• http://en.wikipedia.org/wiki/Power-to-weight_ratio

which gives me some formulas, but its been a long time since I used any maths, and it was way beyond me, especially as there is a certain amount of drag caused by the water.

I do apologize if this question is not relevant to this website.

Answer 1

In SI units, the desired speed is $v = 10\cdot 1000/3600$ (meters per second). The desired acceleration over $7$ seconds (assuming it's uniform) is $v/7$. Given the mass of $120$ kg, you need the force of $120$ times the acceleration, that is $$120 \cdot 10 \cdot \frac{1000}{3600} \frac{1}{7}$$ (measured in Newton). Not much. (The speed of 10 km/hr isn't much, either.)

Answer 2

The equations you need are:

$F = ma$

(the thrust is a force $F$. $m$ is mass. $a$ is the acceleration)

and

$v = u + at$

where $v$ is final velocity, $u$ is initial velocity, $a$ is (constant) acceleration and $t$ is time.

Can you figure it out? Try it first, and post your difficulties in comments. I may expand on my answer then.