Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Problem 69

A baseball is thrown with a velocity of \(31.1 \mathrm{~m} / \mathrm{s}\) at an angle of \(\theta=33.4^{\circ}\) above horizontal. What is the horizontal component of the ball's velocity at the highest point of the ball's trajectory?

Short Answer

Expert verified
Answer: The horizontal component of the ball's velocity at the highest point of its trajectory is approximately 25.96 m/s.

Step by step solution

01

Find the initial velocity components in horizontal and vertical directions

We can find the initial velocity components using the given initial velocity and angle. Initial horizontal component of velocity (u_x): \(u_x = u \cos(\theta)\) Initial vertical component of velocity (u_y): \(u_y = u \sin(\theta)\) where u is the initial velocity (31.1 m/s) and θ is the angle (33.4°).
02

Calculate the initial horizontal component of velocity

Use the formula for the horizontal component: \(u_x = u \cos(\theta)\) \(u_x = 31.1 \times \cos(33.4^{\circ})\) \(u_x \approx 25.96 \mathrm{~m} / \mathrm{s}\) So, the initial horizontal component of the velocity is approximately 25.96 m/s.
03

Calculate the initial vertical component of velocity

Now, use the formula for the vertical component: \(u_y = u \sin(\theta)\) \(u_y = 31.1 \times \sin(33.4^{\circ})\) \(u_y \approx 17.02 \mathrm{~m} / \mathrm{s}\) So, the initial vertical component of the velocity is approximately 17.02 m/s.
04

Identify the horizontal component of the velocity at the highest point of the trajectory

As the horizontal component of the velocity remains constant throughout the entire flight, the horizontal component of the velocity at the highest point of the trajectory will remain the same, i.e., 25.96 m/s. Therefore, the horizontal component of the ball's velocity at the highest point of the trajectory is approximately \(25.96 \mathrm{~m} / \mathrm{s}\).

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 salesman is standing on the Golden Gate Bridge in a traffic jam. He is at a height of \(71.8 \mathrm{~m}\) above the water below. He receives a call on his cell phone that makes him so mad that he throws his phone horizontally off the bridge with a speed of \(23.7 \mathrm{~m} / \mathrm{s}\) a) How far does the cell phone travel horizontally before hitting the water? b) What is the speed with which the phone hits the water?

An outfielder throws a baseball with an initial speed of \(32 \mathrm{~m} / \mathrm{s}\) at an angle of \(23^{\circ}\) to the horizontal. The ball leaves his hand from a height of \(1.83 \mathrm{~m}\). How long is the ball in the air before it hits the ground?

For a given initial speed of an ideal projectile, there is (are) \(\quad\) launch angle(s) for which the range of the projectile is the same. a) only one b) two different c) more than two but a finite number of d) only one if the angle is \(45^{\circ}\) but otherwise two different e) an infinite number of

A projectile is launched at a \(60^{\circ}\) angle above the horizontal on level ground. The change in its velocity between launch and just before landing is found to be \(\Delta \vec{v}=\vec{v}_{\text {landing }}-\vec{v}_{\text {launch }}=-20 \hat{y} \mathrm{~m} / \mathrm{s}\). What is the initial velocity of the projectile? What is its final velocity just before landing?

A diver jumps from a \(40.0 \mathrm{~m}\) high cliff into the sea. Rocks stick out of the water for a horizontal distance of \(7.00 \mathrm{~m}\) from the foot of the cliff. With what minimum horizontal speed must the diver jump off the cliff in order to clear the rocks and land safely in the sea?
See all solutions

Recommended explanations on Physics Textbooks

Solid State Physics

Read Explanation

Electricity and Magnetism

Read Explanation

Astrophysics

Read Explanation

Dynamics

Read Explanation

Turning Points in Physics

Read Explanation

Oscillations

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