8. At time t= 0 seconds a particle is at the origin and has velocity vector (4, 4). It undergoes constant acceleration a(t)= (0,-1). (l Find formulas for the velocity function v(t) and the po- sition function p(t) (h) Plot the path taken by the particle p(t) for 0t<10. What familiar shape does the path seem to have? (c) Eliminate the variable t in the parametric equations for the curve p(t). What is the resulting equation? Does it agree with what you found in the previous part? (d) Find the arclength of the curve p(t) from t = 0 to t =10. [HINT: Set up the integral by hand; either solve it exactly 10 11 a table of integrals or use technology to approxi- using mate the integral numerically] A projectile is at (0, 0) at time t = 0 seconds. Its initial speed is 100 meters per second, its initial angle is T/3, and it travels under free fall conditions 12 (a) Find equations for the velocity and position functions. (b) When does the projectile touch down? (c) Plot the projectile's trajectory from takeoff to landing. (d) At what time is the projectile at maximum height? How high is this? (HINT: Find the time at which the velocity vector is horizontal.] (e) Find the speed and the velocity at the moment the pro- jectile is highest.
8. At time t= 0 seconds a particle is at the origin and has velocity vector (4, 4). It undergoes constant acceleration a(t)= (0,-1). (l Find formulas for the velocity function v(t) and the po- sition function p(t) (h) Plot the path taken by the particle p(t) for 0t<10. What familiar shape does the path seem to have? (c) Eliminate the variable t in the parametric equations for the curve p(t). What is the resulting equation? Does it agree with what you found in the previous part? (d) Find the arclength of the curve p(t) from t = 0 to t =10. [HINT: Set up the integral by hand; either solve it exactly 10 11 a table of integrals or use technology to approxi- using mate the integral numerically] A projectile is at (0, 0) at time t = 0 seconds. Its initial speed is 100 meters per second, its initial angle is T/3, and it travels under free fall conditions 12 (a) Find equations for the velocity and position functions. (b) When does the projectile touch down? (c) Plot the projectile's trajectory from takeoff to landing. (d) At what time is the projectile at maximum height? How high is this? (HINT: Find the time at which the velocity vector is horizontal.] (e) Find the speed and the velocity at the moment the pro- jectile is highest.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Question
Both 8 and 9.
![8. At time t= 0 seconds a particle is at the origin and has
velocity vector (4, 4). It undergoes constant acceleration
a(t)= (0,-1).
(l Find formulas for the velocity function v(t) and the po-
sition function p(t)
(h) Plot the path taken by the particle p(t) for 0t<10.
What familiar shape does the path seem to have?
(c) Eliminate the variable t in the parametric equations for
the curve p(t). What is the resulting equation? Does it
agree with what you found in the previous part?
(d) Find the arclength of the curve p(t) from t = 0 to t =10.
[HINT: Set up the integral by hand; either solve it exactly
10
11
a table of integrals or use technology to approxi-
using
mate the integral numerically]
A projectile is at (0, 0) at time t = 0 seconds. Its initial speed
is 100 meters per second, its initial angle is T/3, and it travels
under free fall conditions
12
(a) Find equations for the velocity and position functions.
(b) When does the projectile touch down?
(c) Plot the projectile's trajectory from takeoff to landing.
(d) At what time is the projectile at maximum height? How
high is this? (HINT: Find the time at which the velocity
vector is horizontal.]
(e) Find the speed and the velocity at the moment the pro-
jectile is highest.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8cc1c819-3e42-4c40-a26b-e0d638082b82%2Fa61409af-9061-4d69-ac44-a99d78fb7bcd%2Fifcnhhj.jpeg&w=3840&q=75)
Transcribed Image Text:8. At time t= 0 seconds a particle is at the origin and has
velocity vector (4, 4). It undergoes constant acceleration
a(t)= (0,-1).
(l Find formulas for the velocity function v(t) and the po-
sition function p(t)
(h) Plot the path taken by the particle p(t) for 0t<10.
What familiar shape does the path seem to have?
(c) Eliminate the variable t in the parametric equations for
the curve p(t). What is the resulting equation? Does it
agree with what you found in the previous part?
(d) Find the arclength of the curve p(t) from t = 0 to t =10.
[HINT: Set up the integral by hand; either solve it exactly
10
11
a table of integrals or use technology to approxi-
using
mate the integral numerically]
A projectile is at (0, 0) at time t = 0 seconds. Its initial speed
is 100 meters per second, its initial angle is T/3, and it travels
under free fall conditions
12
(a) Find equations for the velocity and position functions.
(b) When does the projectile touch down?
(c) Plot the projectile's trajectory from takeoff to landing.
(d) At what time is the projectile at maximum height? How
high is this? (HINT: Find the time at which the velocity
vector is horizontal.]
(e) Find the speed and the velocity at the moment the pro-
jectile is highest.
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