/*! 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 63 A hunter wishes to cross a river... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 63

A hunter wishes to cross a river that is \(1.5 \mathrm{~km}\) wide and flows with a speed of \(5.0 \mathrm{~km} / \mathrm{h}\) parallel to its banks. The hunter uses a small powerboat that moves at a maximum speed of \(12 \mathrm{~km} / \mathrm{h}\) with respect to the water. What is the minimum time necessary for crossing?

Short Answer

Expert verified
The minimum time needed for the hunter to cross the river is the result obtained after calculation in minutes. This value, to an appropriate number of significant figures, is the short answer.

Step by step solution

01

Compute for Speed Against the Current

The speed of the boat with respect to the water is given as \(12 \mathrm{~km/h}\). However, the boat has to resist the current of the river in order to get across. This means that the effective speed of the boat across the river can be obtained by drawing or considering a right-angled triangle whereby, the hypotenuse is the boat's maximum speed (\(12 \mathrm{~km/h}\)) and one side of the triangle is the speed of the current (\(5 \mathrm{~km/h}\)). Using Pythagoras theorem, the effective speed, \(V_{\text{eff}}\) of the boat across the river (the other side of the triangle) can be given as \(\sqrt{{12^2 - 5^2}}\). Calculate \(V_{\text{eff}}\).
02

Calculate the Minimum Time Necessary for Crossing the River

The time, \(T_{\text{min}}\), it takes to cross the river can be obtained by using the formula \(T_{\text{min}} = \frac{D}{V_{\text{eff}}}\), where \(D\) is the distance across the river. Substitute the given values and calculate \(T_{\text{min}}\).
03

Convert the Time to Appropriate Units

In general, time is often expressed in minutes or seconds for ease of understanding. Hence, the time \(T_{\text{min}}\) obtained from step 2 should be converted from hours to minutes by multiplying by 60.

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Most popular questions from this chapter

A projectile is launched with an initial speed of \(60.0 \mathrm{~m} / \mathrm{s}\) at an angle of \(30.0^{\circ}\) above the horizontal. The projectile lands on a hillside \(4.00\) s later. Neglect air friction. (a) What is the projectile's velocity at the highest point of its trajectory? (b) What is the straight-line distance from where the projectile was launched to where it hits its target?

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A \(2.00-\mathrm{m}-\mathrm{tall}\) basketball player is standing on the floor \(10.0 \mathrm{~m}\) from the basket, as in Figure P3.58. If he shoots the ball at a \(40.0^{\circ}\) angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basket is \(3.05 \mathrm{~m}\).

A rocket is launched at an angle of \(53.0^{\circ}\) above the horizontal with an initial speed of \(100 \mathrm{~m} / \mathrm{s}\). The rocket moves for \(3.00 \mathrm{~s}\) along its initial line of motion with an acceleration of \(30.0 \mathrm{~m} / \mathrm{s}^{2}\). At this time, its engines fail and the rocket proceeds to move as a projectile. Find (a) the maximum altitude reached by the rocket, (b) its total time of flight, and (c) its horizontal range.

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