Question

The net force on a boat causes it to accelerate at 1.55 m/s2. The mass of the boat is 215 kg. The same net force causes another boat to accelerate at 0.125 m/s2. (a) What is the mass of the second boat? (b) One of the boats is now loaded on the other, and the same net force is applied to this combined mass. What acceleration does it cause?

Answer 1

Answer:

2666 kg

0.11567 m/s²

Explanation:

m = Mass of boat

a = Acceleration of boat

From Newton's second law

Force

$F=ma\\\Rightarrow F=215\times 1.55\\\Rightarrow F=333.25\ N$

Force on the first boat is 333.25 N

$F=ma\\\Rightarrow m=\frac{F}{a}\\\Rightarrow m=\frac{333.25}{0.125}\\\Rightarrow m=2666\ kg$

Hence, mass of the second boat is 2666 kg

Combined mass = 2666+215 = 2881 kg

$F=ma\\\Rightarrow a=\frac{F}{m}\\\Rightarrow a=\frac{333.25}{2881}\\\Rightarrow a=0.11567\ m/s^2$

The acceleration on the combined mass is 0.11567 m/s²