# A boat that travels 3.00 m/s relative to the water is crossing a river that is 1.00 km wide. The destination on the far side of the river is 0.500 km downstream from the starting point. (a) If the river current is 2.00 m/s, in what direction should the boat be pointed in order to reach the destination? (b) How much time will the trip take?

a) 10.29° upstream

b) t=338.7s

Explanation:

If the river is 1km wide and the destination point is 0.5km away downstream, then the angle and distance the the boat has to travel is:

The realitve velocity of the boat respect to the water is:

where β is the angle it has to be pointed at.

From the relative mvement equations:

where

From this equation we get one equation per the x-axis and another for the y-axis. If we square each of them and add them together, we will get 2 equations:

Solving for V:

V = 3.3m/s   and   V=-1.514m/s   Replacing this value into one of our previous x or y-axis equations:

The amount of time:

## Related Questions

Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 mi/h) when the jet stream descends during early spring. show answer No Attempt Approximately what is the force due to the Bernoulli effect on a roof having an area of 205 m2? Typical air density in Boulder is 1.14 kg/m3 , and the corresponding atmospheric pressure is 8.89 × 104 N/m2 . (Bernoulli’s principle assumes a laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.)

The force exerted on the roof is

Explanation:

From the question we are told that

The speed of the wind is

The area of the roof is

The air density of Boulder is

The atmospheric pressure is

For a laminar flow the Bernoulli’s principle is  mathematically represented as

Where   is the  speed of air in  the building

is the speed of air outside the building

are the pressure of inside and outside the house

are the height above and  below the roof

Now for

The above equation becomes

Since pressure is mathematically represented as

The above equation can be written as

The initial velocity is 0

Substituting value

An implanted pacemaker supplies the heart with 72 pulses per minute, each pulse providing 6.0 V for 0.65 ms. The resistance of the heart muscle between the pacemaker’s electrodes is 550 Ω. Find (a) the current that flows during a pulse, (b) the energy delivered in one pulse, and (c) the average power supplied by the pacemaker.

a) Current = 11 mA

b) Energy = 66 mJ

c) Power = 101.54 W

Explanation:

a) Voltage, V = IR

Voltage, V = 6 V, Resistance, R = 550 Ω

Current, I

b) Energy = Current x Voltage = 6 x 0.011 = 0.066 J = 66 mJ

c)

Two microwave frequencies are authorized for use in microwave ovens: 895 and 2560 mhz. calculate the wavelength of each.

Wavelength = (speed) / (frequency)

The speeds of the two possible signals are equal, just like
all other forms of electromagnetic radiation.

Wavelength of 895 MHz = (3 x 10⁸ m/s) / (8.95 x 10⁸/s) = 0.335 m

Wavelength of 2560 MHz = (3 x 10⁸ m/s) / (2.56 x 10⁹/s) =  0.117 m

Water on Earth was (a) transported here by comets; (b) accreted from the solar nebula; (c) produced by volcanoes in the form of steam; (d) created by chemical reactions involving hydrogen and oxygen shortly after Earth formed.

Answer: Water on Earth was transported here by comets. The correct option is A.

Explanation:

Comets are made up of water with ice, rock and minerals.

Alot of research and hypotheses has been made to prove the origin of water on planet earth. Extraplanetary source such as comets, trans-Neptunian objects, and water-rich meteoroids (protoplanets) are believed to have delivered water to Earth.

A swimmer heads directly across a river, swimming at 1.00 m/s relative to still water. He arrives at a point 41.0 m downstream from the point directly across the river, which is 73.0 m wide. What is the speed of the river current?

velocity of the river is equal to 0.56 m/s

Explanation:

given,

velocity of swimmer w.r.t still water = 1 m/s

width of river = 73 m

he arrives to the point = 41 m

t = 73 s

=

= 0.56 m/s

velocity of the river is equal to 0.56 m/s

A particle (q = 5.0 nC, m = 3.0 μg) moves in a region where the magnetic field has components Bx = 2.0 mT, By = 3.0 mT, and Bz = −4.0 mT. At an instant when the speed of the particle is 5.0 km/s and the direction of its velocity is 120° relative to the magnetic field, what is the magnitude of the acceleration of the particle in m/s2?

The acceleration of the particle is 38.87 kg.

### Net magnetic field

The net magnetic field is calculated as follows;

### Magnetic force on the charge

The magnetic force on the charge is calculated as follows;

### Acceleration of the particle

The acceleration of the particle is calculated as follows;

Explanation:

It is given that,

Charge on the particle,

Mass of the particle,

Magnetic field component,

Net magnetic field,

Speed of the particle, v = 5 km/s = 5000 m/s

Angle between velocity and magnetic field,

Magnetic force is given by :

Acceleration of the particle is given by,

So, the acceleration of the particle is 38.6 m/s². Hence, this is the required solution.