vegetars8t

2022-01-05

Two boats start together and race across a 60-km-wide lake and back. Boat A goes across at 60 km/h and returns at 60 km/h. Boat B goes across at 30 km/h, and its crew, realizing how far behind it is getting, returns at 90 km/h. Turnaround times are negligible, and the boat that completes the round trip first wins. What is the average velocity of the winning boat?

Nadine Salcido

Beginner2022-01-06Added 34 answers

Step 1

Here width of the lake

$w=60km$

Up speed of the boat-1$v}_{1U}=60km\text{}{h}^{-1$

Down speed of the boat-1$v}_{1D}=60km\text{}{h}^{-1$

Up speed of the boat-2$v}_{2U}=30km\text{}{h}^{-1$

Down speed of the boat-2$v}_{2D}=90km\text{}{h}^{-1$

The time taken by the boat-1 for the trip is

$t}_{1}=\frac{w}{{v}_{1U}}+\frac{w}{{v}_{1D}$

1)$=\frac{60km}{60km\text{}{h}^{-1}}+\frac{60km}{60km\text{}{h}^{-1}}$

$=2h$

And the time taken by the boat-2 for the trip is

$t}_{2}=\frac{w}{{v}_{2U}}+\frac{w}{{v}_{2D}$

2)$=\frac{60km}{30km\text{}{h}^{1}}+\frac{60km}{90km\text{}{h}^{-1}}$

$=2.666h$

$=2.7h$

Because from equations (1) and (2), we can see that

$t}_{2}>{t}_{1$

Therefore boat-1 wins the trip by 0.7 h

Because the winning boat-1 returns at the same point from where it stars. Therefore its displacement is zero. So the average velocity of the winning boat-1 is

$\overrightarrow{\stackrel{\u2015}{v}}=\frac{\text{displacement}}{\text{time taken}}$

$=\frac{0}{2h}$

$=0m\text{}{s}^{-1}$

Here width of the lake

Up speed of the boat-1

Down speed of the boat-1

Up speed of the boat-2

Down speed of the boat-2

The time taken by the boat-1 for the trip is

1)

And the time taken by the boat-2 for the trip is

2)

Because from equations (1) and (2), we can see that

Therefore boat-1 wins the trip by 0.7 h

Because the winning boat-1 returns at the same point from where it stars. Therefore its displacement is zero. So the average velocity of the winning boat-1 is

nghodlokl

Beginner2022-01-07Added 33 answers

Step 1

Average speed for boat A equals:

$v}_{a}=\frac{2l}{{t}_{1}}=\frac{120}{2}\frac{km}{h}=60\frac{km}{h$

(and because boat A has constant speed during all trip)

Average speed for boat A equals:

(and because boat A has constant speed during all trip)

karton

Expert2022-01-10Added 613 answers

Step 1

Since boat A starts at starting point of lake and returns back after completing race at the same starting point, So total displacement is zero.

So,

22+64

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