All categories

3 years ago

A boat crosses a 200 m wide river at 3 ms-1, north relative to water. The river flows at 1 ms-1 as shown.

Physics

1 answer:

Vika [28.1K]3 years ago

8 0

Answer:

3.16 m·s⁻¹ at an angle of 71.6°

Explanation:

Assume that the diagram is like Fig. 1 below.

The boat is heading straight across the river and the current is directed straight downstream.

We have two vectors at right angles to each other.

1. Calculate the magnitude of the resultant

We can use the Pythagorean theorem (Fig. 2).

R² = (3 m·s⁻¹)² + (1 m·s⁻¹)² = 9 m²·s⁻² + 1 m²·s⁻² = 10 m²·s⁻²

R = √(10 m²·s⁻²) ≈ 3.16 m·s⁻¹

2. Calculate the direction of the resultant

The direction of the resultant is the counterclockwise angle (θ) that it makes with due East .

tanθ = opposite/adjacent = 3/1 = 3

θ = arctan 3 = 71.6°

To an observer at point O, the velocity of the boat is 3.16 m·s⁻¹ at an angle of 71.6°.

You might be interested in

Drops of rain fall perpendicular to the roof of a parked car during a rainstorm. The drops strike the roof with a speed of 15 m/

IrinaK [193]

Answer: (a) 1.065 N (b) 2.13 N

Explanation:

<h2>(a) average force exerted by the rain on the roof</h2><h2 />

According Newton's 2nd Law of Motion the force $F$ is defined as <u>the variation of linear momentum</u> $p$ <u>in time:</u>

$F=\frac{dp}{dt}$ (1)

Where the linear momentum is:

$p=mV$ (2) Being $m$ the mass and $V$ the velocity.

In the case of the rain drops, which initial velocity is $V_{i}=15m/s$ and final velocity is $V_{f}=0$ (we are told the drops come to rest after striking the roof). The momentum of the drops $p_{drops}$ is:

$p_{drops}=mV_{i}+mV_{f}$ (3)

If $V_{f}=0$ , then:

$p_{drops}=mV_{i}$ (4)

Now the force $F_{drops}$ exerted by the drops is:

$F_{drops}=\frac{dp_{drops}}{dt}=\frac{d}{dt}mV_{i}$ (5)

$F_{drops}=\frac{dm}{dt}V_{i}+m\frac{dV_{i}}{dt}$ (6)

At this point we know the mass of rain per second (mass rate) $\frac{dm}{dt}=0.071 kg/s$ and we also know the initial velocity does not change with time, because that is the velocity at that exact moment (instantaneous velocity). Therefore is a constant, and the derivation of a constant is zero.

This means (6) must be rewritten as:

$F_{drops}=\frac{dm}{dt}V_{i}$ (7)

$F_{drops}=(0.071 kg/s)(15m/s)$ (8)

$F_{drops}=1.065kg.m/s^{2}=1.065N$ (9) This is the force exerted by the rain drops on the roof of the car.

<h2>(b) average force exerted by hailstones on the roof </h2><h2 />

Now let's assume that instead of rain drops, hailstones fall on the roof of the car, and let's also assume these hailstones bounce back up off after striking the roof (this means they do not come to rest as the rain drops).

In addition, we know the hailstones fall with the same velocity as the rain drops and have the same mass rate.

So, in this case the linear momentum $p_{hailstones}$ is:

$p_{hailstones}=mV_{i}+mV_{f}$ (9) Being $V_{i}=V_{f}$

$p_{hailstones}=mV+mV=2mV$ (10)

Deriving with respect to time to find the force $F_{hailstones}$ exerted by the hailstones:

$F_{hailstones}=\frac{d}{dt}p_{hailstones}=\frac{d}{dt}(2mV)$ (10)

$F_{hailstones}=2\frac{d}{dt}(mV)=2(\frac{dm}{dt}V+m\frac{dV}{dt})$ (11)

Assuming $\frac{dV}{dt}=0$ :

$F_{hailstones}=2(\frac{dm}{dt}V)$ (12)

$F_{hailstones}=2(0.071 kg/s)(15m/s)$ (13)

Finally:

$F_{hailstones}=2.13kg.m/s^{2}=2.13N$ (14) This is the force exerted by the hailstones

Comparing (9) and (14) we can conclude the force exerted by the hailstones is two times greater than the force exerted by the raindrops.

5 0

3 years ago

Which describes the image produced by a convex mirror? smaller than the object and right-side up smaller than the object and ups

inessss [21]

Answer:Smaller Than the object and right-side up

Explanation:

6 0

4 years ago

Why are illegal drugs dangerous

Vladimir [108]

Answer:

Illegal drugs are dangerous because once someone starts doing drugs they go insane for more and their demand for my drugs can be so dangerous that they would even sometimes harm the people close to them and, In some cases people start to hate them selves and some even killed themselves.

6 0

3 years ago

Two parallel plates, each having area A = 3557 cm2 are connected to the terminals of a battery of voltage Vb = 6 V as shown. The

Dmitry [639]

Capacitance,C is equal to epsilon times area of the plate divided by distance. The permittivity of air is 8.84 x 10-12 F/m. Capacitance is equal to 2.66 x10^14 F. The energy is equal to 0.5* C*V^2. Substituting, the energy is equal to 0.5* <span> 2.66 x10^14 F * 6^2 V^2 or equal to 4.80 x10^15 W.</span>

8 0

4 years ago

Read 2 more answers

How could you increase the potential energy of the roller coaster shown below?

uysha [10]

It's choice A and B. PE=mgh

5 0

3 years ago

Read 2 more answers