6. A projectile is launched with an initial speed vo at an angle 0 (here 0 <0 < 7/2). The height as a function of time, h(t), is shown in a graph bclow. The equation for h(t) is approximately given by h(t) = -16t + (vo sin 0)t. h(t) (a) Find the maximum height reached. (b) Find the time it takes to reach the ground again. [hint: set h(t) = 0] (c) The distance it travels horizontally as a function of time, r(t), is given by r(t) = (vo cos 0)t. How far has the projectile traveled (horizontally) by the time it reaches the ground again? Call this distance X. [hint: use part (b)]
6. A projectile is launched with an initial speed vo at an angle 0 (here 0 <0 < 7/2). The height as a function of time, h(t), is shown in a graph bclow. The equation for h(t) is approximately given by h(t) = -16t + (vo sin 0)t. h(t) (a) Find the maximum height reached. (b) Find the time it takes to reach the ground again. [hint: set h(t) = 0] (c) The distance it travels horizontally as a function of time, r(t), is given by r(t) = (vo cos 0)t. How far has the projectile traveled (horizontally) by the time it reaches the ground again? Call this distance X. [hint: use part (b)]
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![6. A projectile is launched with an initial speed vo at an angle 0 (here 0SO S T/2). The height
as a function of time, h(t), is shown in a graph below. The cquation for h(t) is approximatcly
given by
h(t) = -16t + (vo sin 0)t.
h(t)
(a) Find the maximum height reachcd.
(b) Find thc time it takes to reach the ground again. hint: sct h(t) = 0]
(c) The distance it travels horizontally as a function of time, r(t), is given by r(t) = (vo cos 0)t.
How far has the projectile traveled (horizontally) by the time it reachcs the ground again?
Call this distance X. [hint: use part (b)I
%3D
(d) Notice the answer to (c) depends on the launch angle 0, so we can think of X as a function
of 0, X (0). Find the angle that will result in the farthest distance traveled. [i.c. which 0
maximizes X(0)?]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F68fa2971-a9f5-43d8-95cd-ab6e882bb92e%2F42b8d882-dad3-4963-a475-227b6def6f66%2Fsljt3m5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. A projectile is launched with an initial speed vo at an angle 0 (here 0SO S T/2). The height
as a function of time, h(t), is shown in a graph below. The cquation for h(t) is approximatcly
given by
h(t) = -16t + (vo sin 0)t.
h(t)
(a) Find the maximum height reachcd.
(b) Find thc time it takes to reach the ground again. hint: sct h(t) = 0]
(c) The distance it travels horizontally as a function of time, r(t), is given by r(t) = (vo cos 0)t.
How far has the projectile traveled (horizontally) by the time it reachcs the ground again?
Call this distance X. [hint: use part (b)I
%3D
(d) Notice the answer to (c) depends on the launch angle 0, so we can think of X as a function
of 0, X (0). Find the angle that will result in the farthest distance traveled. [i.c. which 0
maximizes X(0)?]
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