Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Problem 55

A kid fires a squirt gun horizontally from \(1.6 \mathrm{m}\) above the ground. It hits another kid 2.1 m away square in the back, \(0.93 \mathrm{m}\) above the ground. What was the water's initial speed?

Short Answer

Expert verified
The water's initial speed was approximately \(5.68 \mathrm{m/s}\)

Step by step solution

01

Calculation of the time of flight

Using the equation of motion \(h = ut +(1/2)gt^2\), where \(u\) is the initial vertical velocity, \(g\) is the acceleration due to gravity, \(h\) is the height, and \(t\) is the time. The initial vertical velocity is 0 (because the squirt is fired horizontally) and gravity is -9.8 \(m/s^2\). The height is difference between starting and end point which is \(1.6 m - 0.93 m = 0.67 m\). Solving for \(t\), we get \[t = \sqrt{-2h/g} = \sqrt{-2*(-0.67)/-9.8} \approx 0.37\ s\]
02

Calculation of the initial speed

We use the equation \(s = ut\), where \(s\) is the horizontal distance, \(u\) is the initial horizontal velocity (which is also the initial speed because the squirt is fired horizontally), and \(t\) is the time. Solving for \(u\) we get \[u = s/t = 2.1/0.37 \approx 5.68\ m/s\]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A jet is diving vertically downward at \(1200 \mathrm{km} / \mathrm{h}\). If the pilot can withstand a maximum acceleration of \(5 g\) (i.e., 5 times Earth's gravitational acceleration) before losing consciousness, at what height must the plane start a quarter turn to pull out of the dive? Assume the speed remains constant.

A projectile launched at angle \(\theta\) to the horizontal reaches maximum height \(h .\) Show that its horizontal range is \(4 h /\) tan \(\theta\)

Write an expression for a unit vector at \(45^{\circ}\) clockwise from the \(x\) -axis.

Derive a general formula for the horizontal distance covered by a projectile launched horizontally at speed \(v_{0}\) from height \(h\)

An ion in a mass spectrometer follows a semicircular path of radius \(15.2 \mathrm{cm} .\) What are (a) the distance it travels and (b) the magnitude of its displacement?
See all solutions

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Read Explanation

Classical Mechanics

Read Explanation

Medical Physics

Read Explanation

Dynamics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free