edenconsuelo16
Answered

Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

A robotic vehicle, or rover, is exploring the surface of Mars. The stationary Mars lander is the origin of coordinates, and the surrounding Martian surface lies in the xy-plane. The rover, which we represent as a point, has x- and y-coordinates that vary with time: = 2.0 − (0.25 / 2 ) 2 = (1.0/) + (0.025/ 3 ) 3 () ℎ ′ and distance from the lander at t=2.0s. (B) Find the rover’s displacement and average velocity vectors for the interval t=0.0 s to t=2.0s. (c) Find a general expression for the rover’s instantaneous velocity vector ⃗ . Express ⃗ at in component form and in terms of magnitude and direction​

Sagot :

A) The rover’s coordinates and its distance from the lander at t = 2.0 s are; (1, 4) and 4.1 m

B) The rover’s displacement and average velocity vector during the interval are; s = (-1, 4) and v = (-0.5, 2) m/s

C) The magnitude and direction of the instantaneous velocity are; 2.24 m/s and 117°

What is the displacement and Velocity?

The rover's x and y coordinates are given as;

x = 2.0m − (0.25 m/s²)t²

y = (1.0m/s)t + (0.25 m/s³)t³

A) At t = 2 s, the rovers coordinates are;

x = 2.0m − (0.25 m/s²)2²

x = 1 m

y = (1.0m/s)2 + (0.25 m/s³)2³

y = 4 m

Distance from the lander is;

s = √[(1 - 2)² + 4²]

s = 4.1 m

B) Let us first find the distance coordinates for the interval t = 0.0 s to t = 2.0s. Thus;

s = r - r₀

s = (1 - 2), (4 - 0)

s = (-1, 4)

Thus, average velocity vector is;

v = ¹/₂s

v =  ¹/₂(-1, 4)

v = (-0.5, 2) m/s

C) A general expression for the instantaneous velocity components is;

v_x = -0.5t

v_y = 1 - 0.75t²

Thus, v(2) is;

v_x = -0.5(2) = -1

v_y = 1 - 0.75(2)²

v_y = -2

Instantaneous velocity vector is; v = (-1, -2)

Magnitude of instantaneous Velocity = √(-1² + -2²) = 2.24 m/s

Direction = 180° - tan⁻¹(-2/-1) ≈ 117°

Read more about displacement and velocity at; https://brainly.com/question/4931057

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.