Question
upstudy study bank question image url

An acrobat is fired from a cannon at 59 miles per hour at an angle of \( 44^{\circ} \) with respect to the horizontal. What are the horizontal and vertical components, \( v_{x} \) and \( v_{y} \), of the velocity vector \( \mathbf{v} \) ? \( \mathbf{v}=\left[v_{x}, v_{y}\right]=[ \) Ex:5.67

Ask by Wells Romero. in the United States
Mar 18,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The horizontal component \( v_{x} \) is approximately 42.4 mph, and the vertical component \( v_{y} \) is approximately 41.0 mph.

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Beyond the Answer

To find the horizontal and vertical components of the velocity vector, we use the equations: \[ v_{x} = v \cdot \cos(\theta) \] \[ v_{y} = v \cdot \sin(\theta) \] Plugging in the values, we have: - \( v = 59 \) miles per hour - \( \theta = 44^{\circ} \) Calculating \( v_{x} \): \[ v_{x} = 59 \cdot \cos(44^{\circ}) \approx 59 \cdot 0.7193 \approx 42.41 \text{ miles per hour} \] Calculating \( v_{y} \): \[ v_{y} = 59 \cdot \sin(44^{\circ}) \approx 59 \cdot 0.6956 \approx 41.00 \text{ miles per hour} \] So, the final answer is: \[ \mathbf{v}=\left[v_{x}, v_{y}\right]=[ 42.41, 41.00 ] \]

Related Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy