/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 18 A trolley containing water has t... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 18

A trolley containing water has total mass \(4000 \mathrm{~kg}\) and is moving at a speed of \(40 \mathrm{~m} / \mathrm{s}\). Now water start coming out of a hole at the bottom of the trolley at the rate of \(8 \mathrm{~kg} / \mathrm{s}\). Speed of trolley after \(50 \mathrm{~s}\) is (A) \(44.44 \mathrm{~m} / \mathrm{s}\) (B) \(40 \mathrm{~m} / \mathrm{s}\) (C) \(44 \mathrm{~m} / \mathrm{s}\) (D) \(54.44 \mathrm{~m} / \mathrm{s}\)

Short Answer

Expert verified
The speed of the trolley after 50 seconds is \(44.44 \mathrm{~m} / \mathrm{s}\).

Step by step solution

01

List down the given information

We are given that: 1. Initial mass of the trolley (M1) = 4000 kg 2. Initial speed of the trolley (U1) = 40 m/s 3. Rate of water coming out (R) = 8 kg/s 4. Time (t) = 50 s
02

Calculate the mass of water left in the trolley

Considering the rate at which water is coming out of the trolley and the time after which we need to find the speed of the trolley, we will first find out the mass of water remaining in the trolley. Mass of water coming out = Rate 脳 Time Mass of water coming out = 8 kg/s 脳 50 s = 400 kg So, the mass of the trolley after 50 seconds (M2) = M1 - Mass of water coming out M2 = 4000 kg - 400 kg = 3600 kg
03

Apply conservation of momentum

Using the conservation of momentum principle, the total initial momentum of the trolley system must be equal to the total final momentum of the trolley system. Initial momentum (P1) = M1 脳 U1 P1 = 4000 kg 脳 40 m/s = 160000 kgm/s Final momentum (P2) = M2 脳 U2 (where U2 is the final speed of the trolley) According to the conservation of momentum principle, P1 = P2.
04

Solve for U2

Re-writing the equation in terms of U2: \(U2 = \frac{P1}{M2}\) Substitute the values of P1 and M2 from previous steps: \(U2 = \frac{160000 \mathrm{~kgm/s}}{3600 \mathrm{~kg}} \) U2 = 44.44 m/s The speed of the trolley after 50 seconds is 44.44 m/s. Therefore, the correct answer is (A) 44.44 m/s.

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