Question

You are stuck in a boat in the middle of a lake. Luckily, you brought your Physics book! You decide to use your book to propel you back to the shore. You throw your 1 kg book overboard with a speed of 10 m/s to propel yourself back towards the shore. Assume the combined mass of you and the boat is 100 kg. (i) How long would it take you to reach the shore which is 60 m away from the boat after throwing your book? (Ignore friction between the water and the boat.) (ii) It starts raining as you float towards the shore. The rain falls straight down into the boat. 10 kg of rainwater has accumulated at the bottom of your boat. What is your speed now?

Answer 1

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Answer 2

Given:

Mass of the book $m_{1}$ = 1 kg

Mass of the boat $m_{2}$ = 100 kg

Velocity of the book $v_{1}$ = 10 m/s

Distance to reach the shore, d = 60 m

Mass of the rainwater $m_{3}$ = 10 kg

To find:

We have to find:

1. The time taken to reach the shore t.
2. The speed after rainwater is added $v_{3}$ .

Solution:

1) In order to determine the time taken to reach the shore we need to find the speed of the boat.

The speed of the boat can be calculated using the law of conservation of momentum.

By the law of conservation of momentum,

$m_{1}v_{1} = m_{2}v_{2}$

$\[1\times 10 = 100\times v_{2}\]$

$v_{2} = \frac{10}{100} = 0.1 m/s$

Time to reach the shore t = distance/velocity = d/$v_{2}$ = 60/0.1 = 600 seconds

2)The speed of the boat after rainwater is accumulated can also be calculated by using the conservation of momentum.

$m_{2}v_{2} = (m_{2}+m_{3})v_{3}$

$\[100\times 0.1 = (100+10)\times v_{3}\]$

$v_{3} = \frac{10}{110}$

$v_{3} = 0.09m/s$

Thus,

1) The time taken to reach the shore is 600 seconds.

2) The speed of the boat after rain is accumulated is 0.09 m/s.