A projectile (such as a baseball or a cannonball) launched from the origin with an initial horizontal velocity, uo, and an initial vertical velocity, Vo, moves in a parabolic trajectory given by x=uot, y = -9₁² + Vot, for t2 0, where air resistance is neglecte 2 and g≈ 9.8m/s is the acceleration due to gravity. Let uo = 22 m/s and vo= 35 m/s. Complete parts (a) through (d) below. CTU
A projectile (such as a baseball or a cannonball) launched from the origin with an initial horizontal velocity, uo, and an initial vertical velocity, Vo, moves in a parabolic trajectory given by x=uot, y = -9₁² + Vot, for t2 0, where air resistance is neglecte 2 and g≈ 9.8m/s is the acceleration due to gravity. Let uo = 22 m/s and vo= 35 m/s. Complete parts (a) through (d) below. CTU
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer each part,
Thank you
Transcribed Image Text:A projectile (such as a baseball or a cannonball) launched from the origin with an initial horizontal velocity, uo, and an initial
gt²
+ Vot, for t2 0, where air resistance is neglected
vertical velocity, Vo, moves in a parabolic trajectory given by x=uot, y =
and g~ 9.8m/s² is the acceleration due to gravity.
Let uo = 22 m/s and vo = 35 m/s. Complete parts (a) through (d) below.
a. Assuming the projectile is launched over horizontal ground, at what time does it return to Earth?
S.
The projectile returns to Earth at t
(Round to three decimal places as needed.)
b. Find the integral that gives the length, L, of the trajectory from launch to landing.
OA.
OC.
4,9
√ √96.04t² + 1709 dt
0
O G.
171.5
0
7.143
E. √96.04t²
0
7.143
96.041²
0
- 686t+ 1709 dt
+ 1709 dt
√26.011-343t³ +1709t² dt
OB.
OD.
4,9
OH.
0
7.143
0
√26.011* - 3431³ +17091² dt
171.5
OF. √26.01-343t³ +1709t² dt
0
4,9
√96.041-686t+1709 dt
√96.041² - 66t + 1709 dt
c. Evaluate the integral in part (b) by using a calculator. What is the length of the trajectory?
The length of the trajectory is approximately m.
(Round to two decimal places as needed.)
d. How far does the projectile land from its launch site?
The projectile lands approximately Im from the launch site.
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