Ask question

Ask question

All categories

3 years ago

10

You and your friends find a rope that hangs down 19m from a high tree branch right at the edge of a river. You find that you can

run, grab the rope, swing out over the river, and drop into the water. You run at 2.0 m/s and grab the rope, launching yourself out over the river.How long must you hang on if you want to drop into the water at the greatest possible distance from the edge?

1 answer:

tangare [24]3 years ago

5 0

Answer:

Explanation:

Given

length of rope $L=19\ m$

velocity while running $v=2\ m/s$

when the person jumps off the bank and hang on the rope then we can treat the person as pendulum with Time period T which is given by

$T=2\pi \sqrt{\frac{L}{g}}$

$T=2\pi \sqrt{\frac{19}{9.8}}$

$T=2\pi \times 1.392$

$T=8.74\ m/s$

Greatest Possible distance will be covered when person reaches the other extreme end of assumed pendulum (velocity=zero)

therefore he must hang on for 0.5 T time

$time=0.5\times 8.74=4.37\ s$

You might be interested in

A projectile is shot directly away from Earth's surface. Neglect the rotation of the Earth. What multiple of Earth's radius RE g

7nadin3 [17]

Answer:

(a) r = 1.062·R $_E$ = $\frac{531}{500} R_E$

(b) r = $\frac{33}{25} R_E$

(c) Zero

Explanation:

Here we have escape velocity v $_e$ given by

$v_e =\sqrt{\frac{2GM}{R_E} }$ and the maximum height given by

$\frac{1}{2} v^2-\frac{GM}{R_E} = -\frac{GM}{r}$

Therefore, when the initial speed is 0.241v $_e$ we have

v = $0.241\times \sqrt{\frac{2GM}{R_E} }$ so that;

v² = $0.058081\times {\frac{2GM}{R_E} }$

v² = ${\frac{0.116162\times GM}{R_E} }$

$\frac{1}{2} v^2-\frac{GM}{R_E} = -\frac{GM}{r}$ is then

$\frac{1}{2} {\frac{0.116162\times GM}{R_E} }-\frac{GM}{R_E} = -\frac{GM}{r}$

Which gives

$-\frac{0.941919}{R_E} = -\frac{1}{r}$ or

r = 1.062·R $_E$

(b) Here we have

$K_i = 0.241\times \frac{1}{2} \times m \times v_e^2 = 0.241\times \frac{1}{2} \times m \times \frac{2GM}{R_E} = \frac{0.241mGM}{R_E}$

Therefore we put $\frac{0.241GM}{R_E}$ in the maximum height equation to get

$\frac{0.241}{R_E} -\frac{1}{R_E} =-\frac{1}{r}$

From which we get

r = 1.32·R $_E$

(c) The we have the least initial mechanical energy, ME given by

ME = KE - PE

Where the KE = PE required to leave the earth we have

ME = KE - KE = 0

The least initial mechanical energy to leave the earth is zero.

3 0

3 years ago

Read 2 more answers

If two 100 ohms resistors are placed in series, their total resistance is what?

Sindrei [870]

Answer:

add the Resistance

2(100)= 200

2) 200 ohms

3 0

3 years ago

A truck was carrying a substance in a tank. The molecules of that substance were moving away from each other. The truck parked o

DochEvi [55]

Answer:

In the morning the molecules were moving away from each other with a smaller speed than when the truck was carrying the substance.

Explanation:

5 0

3 years ago

After an initial race George determines that his car loses 35 percent of its acceleration due to air resistance travelling at 38

ddd [48]

Answer:

64.2 m/s

Explanation:

We are given that

Speed ,v=38 m/s

We have to find the maximum speed when his car reach on flat ground.

Using dimensional analysis

$F_{res}\propto v^2$

If 35% acceleration reduced by F(res) at 38 m/s

Then, 100% acceleration can be reduced by F(res) at v' m/s

$\frac{F_1}{F_2}=\frac{v^2}{v'^2}$

$v'^2=\frac{F_2}{F_1}v^2$

$v'=v\sqrt{\frac{F_2}{F_1}}$

Substitute the values

$v'=38\times \sqrt{\frac{100}{35}}$

$v'=64.2 m/s$

Hence, the maximum speed when his car can reach on flat ground=64.2 m/s

3 0

3 years ago

If Sherry took her pulse for 6 seconds and felt 14 beats, What would her heart rate be?

Schach [20]

Answer:

140 beats per minute

Explanation:

There are 60 seconds in a minute and we know that Sherry felt 14 beats in 6 seconds if you multiply 6 by 10 you get 60 seconds which can be 1 minute. Then you multiply 14 by 10 since you 14 by 10 since you multiplied 6 by 10 and you get 140 beats per minute.

5 0

3 years ago