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Vlada [557]
3 years ago
6

Running at maximum speed, it takes a boat times as long to go 10 miles upstream as it does to go 10 miles downstream. If the cur

rent is 4 mph, find the speed of the boat in still water.
Physics
1 answer:
Greeley [361]3 years ago
7 0

Note: <em>The question states the time to go upstream is a number of times (not explicitly written) the time to go downstream. We'll assume a general number N</em>

Answer:

\displaystyle v_b=\frac{N+1}{N-1}(4\ mph)

Explanation:

<u>Relative Speed</u>

If a boat is going upstream against the water current, the true speed of motion is v_b-v_w, being v_b the speed of the boat and v_w the speed of the water. If the boat is going downstream, the true speed becomes v_b+v_w.

The question states the time to go upstream is a number of times N (not explicitly written) the time to go downstream. The speed of an object is computed as

\displaystyle v=\frac{x}{t}

Where x is the distance traveled and t the time taken for that. The time can be computed by

\displaystyle t=\frac{x}{v}

If t_u is the time for the upstream travel and t_d is the time for the downstream travel, then

t_u=Nt_d

Siince the same distance x= 10 miles is traveled in both cases:

\displaystyle \frac{10}{v_b-v_w}=N\frac{10}{v_b+v_w}

Simplifying and rearrangling

v_b+v_w=N(v_b-v_w)

Operating

v_b+v_w=Nv_b-Nv_w

Solving for v_b

\displaystyle v_b=\frac{N+1}{N-1}v_w

If\ N=2,\ v_w=4\ mph

\displaystyle v_b=\frac{3}{1}(4)=12\ mph

If N=3

\displaystyle v_b=\frac{4}{2}v_w=2(4)=8\ mph

We can use the required value of N to compute the speed of the boat as explained

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Explanation:

Reactants ⇒ product + heat (exothermic reaction) ....(1)

We have given that the reaction is exothermic, so the heat is rejected from the reaction. We know that heat is the form of energy.

From equation (1)

from the given equation we can see that reactants have more energy than products.

So the reactants have higher potential energy in comparison to the products.

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3 years ago
A weight trainer lifts a 90.0-kg barbell from a stand 0.90 m high and raises it to a height of 1.75 m. What is the increase in t
nirvana33 [79]

Answer:

∆PE = 749.7 J

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2 years ago
What is an essential characteristic of an object in equilibrium?
bulgar [2K]

Answer:

2) zero acceleration

Explanation:

Motion can be defined as a change in the location (position) of a physical object or body with respect to a reference point.

This ultimately implies that, motion would occur as a result of a change in location (position) of an object with respect to a reference point or frame of reference i.e where it was standing before the effect of an external force.

Mathematically, the motion of an object is described in terms of time, distance, speed, velocity, position, displacement, acceleration, etc.

In physics, acceleration can be defined as the rate of change of the velocity of an object with respect to time.

Generally, an object is said to be in equilibrium when neither the energy possessed by the object not state of motion changes with respect to time. Thus, the vector sum of all the forces acting upon an object that's in equilibrium is zero.

In conclusion, an essential characteristic of an object in equilibrium is zero (0) acceleration because there's no change in its velocity with respect to time.

5 0
3 years ago
A heavy ball with a weight of 150 N is hung from the ceiling of a lecture hall on a 4.1-m-long rope. The ball is pulled to one s
AlladinOne [14]

Answer:

The tension in the rope is 262.88 N

Explanation:

Given:

Weight W = 150 N

Length of rope r = 4.1 m

Initial speed of ball v = 5.5 \frac{m}{s}

For finding the tension in the rope,

First find the mass of rod,

mg = 150                          ( g = 9.8 \frac{m}{s^{2} } )

  m = \frac{150}{9.8}

  m = 15.3 kg

Tension in the rope is,

  T = mg + \frac{mv^{2} }{r}

  T = 150 + \frac{15.3 \times (5.5)^{2} }{4.1}

  T = 262.88 N

Therefore, the tension in the rope is 262.88 N

7 0
3 years ago
A meter stick A hurtles through space at a speed v = 0.25c relative to you, with its length aligned with the direction of motion
yaroslaw [1]

Answer:

L_0\approx1.0328\ m

Explanation:

Given:

  • relativistic length of stick A, L=1\ m
  • relativistic velocity of stick A with respect to observer, v=0.25c=7.5\times 10^{7}\ m.s^{-1}

<em>Since the object is moving with a velocity comparable to the velocity of light  with respect to the observer therefore the length will appear shorter according to the theory of relativity.</em>

<u> Mathematical expression of the theory of relativity for length contraction:</u>

L=\frac{L_0}{\gamma}

where:

L = relativistic length

L_0= original length at rest

\gamma = Lorentz factor =\frac{1}{\sqrt{1-\frac{v^2}{c^2} } }

\Rightarrow 1=\frac{L_0}{\frac{1}{\sqrt{1-\frac{(0.25c)^2}{c^2} } }}

L_0=\frac{1}{\sqrt{1-\frac{(0.25c)^2}{c^2} } }

L_0\approx1.0328\ m

4 0
3 years ago
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