Physics, 28.09.2019 13:00 cobalt426

Aboat of mass 115 kg drifts along a river at a speed of 13 m/s to the east. what impulse is required to decrease the speed of the boat to 10 m/s to the east?

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M = 115 kg.

Final velocity, v = 10 m/s to the east

Initial Velocity, u = 13 m/s to the east

Impulse = m(v - u)

= 115*(10 - 13)

= 115*-3 = -345 kgm/s or -345 Ns

Answer from: cabr379

An impulse of $\boxed{345\text{ N}\cdot\text{s}}$ to the west is required to decrease the speed of the boat from $13\text{ m/s}$ east to $10\text{ m/s}$ east.

Further explanation:

When a force acted upon an object for a very small time, is called impulse. Force is a rate of change of momentum with respect to time. Therefore if momentum associated with an object is changed in a very short time, the force exerted on the object is called the impulse.

Given:

Mass of the boat is $115\text{ kg}$ .

Initial speed of the boat is $13\text{ m/s}$ to the east.

Final velocity of the boat is $10\text{ m/s}$ to the east.

Concept:

Let’s assume east direction as the positive direction of x axis.

Write the expression for impulse

$\begin{aligned}I&={{\vec F}_{{\text{avg}}}}\cdot\Delta t\\&=\Delta m\vec V\\\end{aligned}$

Here, is the impulse force, $\Delta m\vec V$ is the change of momentum, $\Delta t$ is the time and is the mass of the boat.

In the above expression is a constant, therefore above expression can be rewritten as

$I=m\cdot\Delta\vec V$ …… (1)

Here, $\Delta\vec V$ is the change in the velocity of the boat.

Write the expression for change in velocity

$\Delta\vec V={V_{\text{f}}}-{V_{\text{i}}}$ …… (2)

Here, ${V_{\text{f}}}$ is the final velocity of boat and ${V_{\text{i}}}$ is the initial velocity of the boat.

Substitute $13\text{ m/s}$ for ${V_{\text{i}}}$ and $10\text{ m/s}$ for ${V_{\text{f}}}$ in equation (2).

$\begin{aligned}\Delta \vec V&=\left( {10\,\hat i}\right)-\left( {13\,\hat i}\right)\\&=3\,\left({-\hat i}\right)\\\end{aligned}$

Substitute $3\,{\text{m/s}}\,\left( { - \hat i} \right)$ for $\Delta \vec V$ and $115\text{ kg}$ for in equation (1).

$\begin{aligned}I&=\left({115\,{\text{kg}}}\right)\left( {-3\,{\text{m/s}}\,\hat i}\right)\\&=345\,{\text{N.s}}\left({-\hat i} \right)\\\end{aligned}$

Here, indicate that the impulse acts in opposite of east direction.

Thus, an impulse of $\boxed{345\text{ N.s}}$ to the west is required to decrease the speed of the boat from $13\text{ m/s}$ east to $10\text{ m/s}$ east.

Learn More:

1. Calculate the net force on Earth due to Venus, mars and jupiter

2. The maximum force to be exerted on a wooden crate to move it with acceleration

3. Conservation of momentum during collision

Answer Details:

Grade: High School

Subject: Physics

Chapter: Force

Keywords:

Boat, mass, 115 kg, drifts, river, 13 m/s, 13 meter per second, east, impulse, decrease, speed, 10 m/s, 10 meter per second, 345 Ns, west, 3.45 times 10^2 Ns.

Aboat of mass 115 kg drifts along a river at a speed of 13 m/s to the east. what impulse is required

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Aboat of mass 115 kg drifts along a river at a speed of 13 m/s to the east. what impulse is required...

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