# Question bb36d

##### 1 Answer
Jun 12, 2015

The second boat has a mass of 2670 kg.

#### Explanation:

You know that force is equal to mass multiplied by acceleration.

Notice that, compared with the acceleration of the first boat, the acceleration of the second boat dropped significantly.

Since the force acting on the two boats is unchanged, this implies that the mass of the second boat must be significantly bigger than the mass of the first boat.

Mathematically, you can write

$F = {m}_{1} \cdot {a}_{1}$, where

$F$ - the force that acts on the two boats;
${m}_{1}$ - the mass of the first boat;
${a}_{1}$ - the mass of the second boat.

Since the same force acts on both boats, you can also write

$F = {m}_{2} \cdot {a}_{2}$, where

${m}_{2}$ - the mass of the second boat;
${a}_{2}$ - the acceleration of the second boat.

As a result, you have

${m}_{1} \cdot {a}_{1} = {m}_{2} \cdot {a}_{2}$

Solve this equation for ${m}_{2}$ to get

m_2 = m_1 * a_1/a_2 = "215 kg" * (1.55cancel("m/s"^(-2)))/(0.125cancel("m/s"^(-2))#

${m}_{2} = \text{2666 kg}$

Rounded to three sig figs, the answer will be

${m}_{2} = \textcolor{g r e e n}{\text{2670 kg}}$