A space shuttle’s coordinates as functions of time are given by x(t) = 7.0 t^3 and y(t) = 4.0t^2 - 2.1t , where x and y are in meters and t is in seconds. Write a vector expression for the ball’s velocity as a function of time

A space shuttle’s coordinates as functions of time are given by x(t) = 7.0 t^3 and y(t) = 4.0t^2 - 2.1t , where x and y are in meters and t is in seconds. Write a vector expression for the ball’s velocity as a function of time

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section1.8: Some Properties Of Vectors

Problem 1.4QQ

See similar textbooks

Related questions

Q: A space shuttle’s coordinates as functions of time are given by x(t) = 7.0 t^3 and y(t) = 4.0t^2 -…

A: Coordinates of space shuttle are given: x - coordinate (x) = 7t3…

Q: A runaway cat walks 0.75 km due north. It runs due west to a hotdog stand. If the magnitude of the…

A: Correct answer is option (D) i.e. 0.66 km

Q: The acceleration of a particle moving only on a horizontal xy plane is given by d = 6tî + 7tj, where…

A: The given values are, a→=6ti^+7tj^ m/s2r→=15.0i^+35.0j^ mv→=6.40i^+3.30j^ m/st=5.60 s

Q: A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time…

A: We are authorized to answer only one question at a time, since you have not mentioned which one…

Q: An object travels along the vector d1 = 4m į + 5m j and then along the vector d2 = 2m į - 3m j. How…

Q: what is the magnitude and direction of the vector formed from the following x and y components? Vx=…

Q: Vector A has a magnitude of 2.00 m and vector B has a magnitude of 5.00 m. If the direction of each…

Q: Suppose you have three vectors: A⃗=−3i^+6j^ B⃗=2i^−4j^ C⃗=4i^+3j^ What is the magnitude of vector…

Q: Starting from a location with position vector r1x = -16.9 m and r1.y = 26.5 m, a rabbit hops around…

Q: Vector A has a magnitude of 8 units and makes an angle of 45.0 degrees with the positive x-axis.…

Q: What are the x and y components of the vector shown below? |A| = 25.5 km 60° Select one: a. x=…

Q: Assuming that up is north, what is the displacement between points F and A? Remember that…

Q: B (15.0 m) Ď (10.0 m) |30.0 53.0 25.0° (12.0 m) Å (8.00 m)

A: |A|=8 m|B|=15 m|C|=12 m|D|=10 m Taking the positive x axis as reference the angles are…

Q: Vector Å has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis.…

A: Given information: Here A is the magnitude of the vector A and θ is the angle made by the vector A…

Q: Starting from a location with position vector r1x = -18.3 m and r1.y = 21.7 m, a rabbit hops around…

A: The initial position of the rabbit, r1,x = -18.3 m and r1,y = 21.7 m The average velocity of the…

Q: Two vectors, of magnitude 30 and 60 respectively, are added. Which one of the following choices is a…

A: The magnitude of the 1st vector is R1 = 60 units The magnitude of 2nd vector is R2 = 30 units

Q: for vector A=1.00i-2.00j and b=3.00i+4.00 jwhat are the magnitude and direction of vector c= A +B

A: Addition of two vectors A→=axi^+ayj^+azk^ and B→=bxi^+byj^+bzk^ is given by-…

Q: If a resultant vector has an x-component of -43cm and a y-component of 34cm, what is the direction…

Q: A car goes east at 90 km/h for 0.75 hours, and then turns on a road heading 30° north of east at 88…

A: Given data The speed of the car in the east direction is vOA = 90 km/h The duration of the car…

Q: A car travels 12km due west, 15km due south and 45 km in a direction 50° north of east. Calculate…

A: Vectors: A vector is quantity which has both magnitude and direction.Magnitude defines the size of…

Q: A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time…

Q: Vector A has a magnitude of 8 units and makes an angle of 45.0 degrees with the positive x-axis.…

A: Given : A→ = 42 i^ + 42 j^ B→ = - 8 i^

Q: A postal employee drives a delivery truck over the route shown in Fig. E1.25. Use the method of…

Q: Given that vectors T = + 2.00x + 6.00y – 4.00z and D = 2.00x – 3.00y – 4.00z…

Q: Vector A is 3 units in length and points along the positive x-axis; vector B is 4 units in length…

Q: Two vectors, of magnitudes 20 mm and 50 mm, are added together. Which one of the following is a…

A: The magnitude of one of the vector = 20 mm The magnitude of other vector = 50 mm

Q: A grasshopper makes four jumps. The displacement vectors are (1) 27.0 cm, due west; (2) 23.0 cm, 35o…

A: Consider a vector (A) in the XY-plane as shown below: It makes an angle (θ) with the x-axis and…

Q: Vector a has a magnitude of 12 units and makes a 60° angle with the +x axis. What is the y component…

A: The y component of vector α is αy=αsinθ Here α=12 units and θ=60o

Q: A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time…

A: Given: x=(18.0 m/s)ty=(4.0 m/s)t-(4.90 m/s2)t2

Q: The velocity vector V1 has a magnitude of 3.0 m/s and is directed along the +x-axis. The velocity…

A: The magnitude of V3 can be 6 m/s, this statement is FALSE.The magnitude of V3 can be 3 m/s, this…

Q: Given vectors A, B and C with components of A,=10 m, Ay=33 m, B,=28 m, B,=25 m, C=-14 m and C,=-13…

Q: If vector B is added to vector i, the result is 6i + j. If B is subtracted from A, the result is -4i…

A: The solution can be given as follows :-

Q: The coordinates of an object moving in the xy plane vary with time according to the equations…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: A space shuttle’s coordinates as functions of time are given by x(t) = 7.0 t^3 and y(t) = 4.0t^2 -…

Q: What is the x-component of a vector with a magnitude of 73 cm, 41° South of east? O 54.89 m, North O…

A: Given value--- Vector A = 73 cm , 41 degree South of east. We have to find --- x component of A.

Q: A particle is moving in three dimensions and its position vector is given by; 7(t) = (1.9t² + 2.1t)…

Q: 1. The coordinates of a particle moving in the XY plane are given as function of time by: X = 5m + (…

Q: A lift is coming from 8th floor and is just about to reach 4th floor. Taking ground floor as origin…

A: c) When a lift is coming down it is moving under the force of gravity , thus the with a positive…

Q: The position vector 7 = 4.70t|i+ let + ft2 is in meters, t is in seconds, and factors e and f are…

A: The angle of direction of motion is written as θ=tan-1vyvx Where, vy is the velocity in y direction…

Q: Axis vectors are vectors that have only one nonzero component. Answer the following questions…

A: WE KNOW THAT In cartesian coordinate system, the magnitude of a vector having…

Q: A car travels 12km due west, 15km due south and 45 km in a direction 50° north of east. Calculate…

A: Suppose given that Vector is R and it makes angle with +x-axis, then it's components are given by:…

Q: A grasshopper makes four jumps. The displacement vectors are (1) 27.0 cm, due west; (2) 23.0 cm, 35o…

A: Given data: The first displacement vector of grass hopper towards west is A=27.0 cm. The second…

Q: Starting from a location with position vector r1x = -18.3 m and r1.y = average velocity Vav.x =…

Q: What is the magnitude of the resultant of vector A moving 21 km/hr, north and vector B heading 12…

Q: A snowmobile is originally at the point with position vector 30.5 m at 95.0° counterclockwise from…

A: Write down the given values using suitable variables. Here r signifies initial position vector, u…

Q: If you know the magnitude of a velocity vector is V, and the angle 0 it makes with horizontal axis…

A: Magnitude = V

Q: Melinda is taking a tour through a new city. On the tour, she walks 0.40 miles south, 0.65 miles…

Q: What is the sum of the following four vectors in (a) unit-vector notation, and as (b) a magnitude…

A: A→=(2.00m)i^+(3.00m)j^ B→= 4.00 m, at 65.0° = 4 ×[ cos65oi^ + sin65oj^]= 1.69i^ + 3.62j^ m…

Concept explainers

Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.

Question

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

What is the y component of the vector (3i8k) m/s? (a) 3 m/s (b) 8 m/s (c) 0 (d) 8 m/s (e) none of those answers
Vector A has x and y components of 8.70 cm and 15.0 cm, respectively; vector B has x and y components of 13.2 cm and 6.60 cm, respectively. If AB+3C=0, what are the components of C?
Three displacement vectors of a croquet ball are shown in Figure P1.44, where |A|=20.0units, |B|=40.0units, and |C|=30.0units. Find (a) the resultant in unit-vector notation and (b) the magnitude and direction of the resultant displacement. Figure P1.44
A space shuttle’s coordinates as functions of time are given by x(t) = 7.0 t^3 and y(t) = 4.0t^2 - 2.1t , where x and y are in meters and t is in seconds. write a vector expression for the ball's position as a function of time.
A space shuttle’s coordinates as functions of time are given by x(t) = 7.0 t^3 and y(t) = 4.0t^2 - 2.1t , where x and y are in meters and t is in seconds. write a vector expression for the ball's acceleration as a function of time.
The equation r(t) = ( sin t)i + ( cos t)j + (t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. π Then write the particle's velocity at t= as a product of its speed and direction. The velocity vector is v(t) = (i+j+ k.
An electron's position is given by r=(ti+t2j+2k) with t in seconds and r in meters. A)Determine the electron's velocity v(t) in unit vector notation. B)What is the magnitude of v(t) at t=2 s? C)What is the angle between v(t) and the unit vector ı ?
Vectors u = −10i + 3j and v = −7i − 9j. What is u − v? a −17i − 6j b 17i + 6j c 3i − 12j d −3i + 12j
As it passes over Grand Bahama Island, the eye of a hurricane is moving in a direction 63.0° north of west with a speed of 40.2 km/h. (Let i represent east and j represent north.) (a) What is the unit-vector expression for the velocity of the hurricane? km/h i+ km/hi It maintains this velocity for 3.50 h, at which time the course of the hurricane suddenly shifts due north, and its speed slows to a constant 25.2 km/h. This new velocity is maintained for 1.50 h. (b) What is the unit-vector expression for the new velocity of the hurricane? km/h j km/h i+ (c) What is the unit-vector expression for the displacement of the hurricane during the first 3.50 h? km i+ km j (d) What is the unit-vector expression for the displacement of the hurricane during the latter 1.50 h? km i+ km j (e) How far from Grand Bahama is the eye 5.00 h after it passes over the island? km
Katherine goes on an adventure to the tower beyond the Aguna forest. She starts her trip by travelling 25 km 45 degrees south of east and camps to spend the night. On the next day, Katherine continues her journey by following 60 degrees north of east, which is 40 km long, and finally reaches the tower. Determine the magnitude and direction of Katherine’s resultant displacement. Also, express the resultant displacement in terms of unit vectors.
Given vector A = (3.00i - 2.00j)m and vector B = (-2.00i + 2.00j)m determine vector C if C = 3A - B. Answers should have three significant figures and each component should have units. Remember to leave a space between your numerical values and the units.
Vector A S has magnitude 8.00 m and is in the xy-plane at an angle of 127 counterclockwise from the +x–axis (37˚ past the +y-axis). What are the magnitude and direction of vector B vec if the sum A vec + B vec is in the -y-direction and has magnitude 12.0 m?