60. Show that for motion in a straight line with constant accelera- tion a, initial velocity vo, and initial displacement so, the dis- placement after time t is =at² + vot + So S= 68.
60. Show that for motion in a straight line with constant accelera- tion a, initial velocity vo, and initial displacement so, the dis- placement after time t is =at² + vot + So S= 68.
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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Question 60
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### Chapter 3: Applications of Differentiation
#### Exercise Problems
**57.** Given \( a(t) = 10 \sin t + 3 \cos t \), \( s(0) = 0 \), \( s(2\pi) = 12 \).
**58.** Given \( a(t) = t^2 - 4t + 6 \), \( s(0) = 0 \), \( s(1) = 20 \).
**59. A stone is dropped from the upper observation deck (the Space Deck) of the CN Tower, 450 m above the ground.**
- (a) Find the distance of the stone above ground level at time \( t \).
- (b) How long does it take the stone to reach the ground?
- (c) With what velocity does it strike the ground?
- (d) If the stone is thrown downward with a speed of 5 m/s, how long does it take to reach the ground?
**60.** Show that for motion in a straight line with constant acceleration \( a \), initial velocity \( v_0 \), and initial displacement \( s_0 \), the displacement after time \( t \) is
\[
s = \frac{1}{2} at^2 + v_0 t + s_0
\]
**61.** An object is projected upward with initial velocity \( v_0 \) meters per second from a point \( s_0 \) meters above the ground. Show that
\[
[v(t)]^2 = v_0^2 - 19.6 [s(t) - s_0]
\]
**62.** Two balls are thrown upward from the edge of the cliff in Example 7. The first is thrown with a speed of 48 ft/s and the other is thrown a second later with a speed of 24 ft/s. Do the balls ever pass each other?
**63.** A stone was dropped off a cliff and hit the ground with a speed of 120 ft/s. What is the height of the cliff?
**64.** If a diver of mass \( m \) stands at the end of a diving board with length \( L \) and linear density \( \rho \), then the board takes on the shape of a curve \( y = f(x) \), where
\[
EI y'' = mg](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F613af2f8-f901-4d4b-81fe-790ed0ca6df6%2Fca5d2f4a-dd82-42bc-967c-da1946422628%2Fjuzla8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Chapter 3: Applications of Differentiation
#### Exercise Problems
**57.** Given \( a(t) = 10 \sin t + 3 \cos t \), \( s(0) = 0 \), \( s(2\pi) = 12 \).
**58.** Given \( a(t) = t^2 - 4t + 6 \), \( s(0) = 0 \), \( s(1) = 20 \).
**59. A stone is dropped from the upper observation deck (the Space Deck) of the CN Tower, 450 m above the ground.**
- (a) Find the distance of the stone above ground level at time \( t \).
- (b) How long does it take the stone to reach the ground?
- (c) With what velocity does it strike the ground?
- (d) If the stone is thrown downward with a speed of 5 m/s, how long does it take to reach the ground?
**60.** Show that for motion in a straight line with constant acceleration \( a \), initial velocity \( v_0 \), and initial displacement \( s_0 \), the displacement after time \( t \) is
\[
s = \frac{1}{2} at^2 + v_0 t + s_0
\]
**61.** An object is projected upward with initial velocity \( v_0 \) meters per second from a point \( s_0 \) meters above the ground. Show that
\[
[v(t)]^2 = v_0^2 - 19.6 [s(t) - s_0]
\]
**62.** Two balls are thrown upward from the edge of the cliff in Example 7. The first is thrown with a speed of 48 ft/s and the other is thrown a second later with a speed of 24 ft/s. Do the balls ever pass each other?
**63.** A stone was dropped off a cliff and hit the ground with a speed of 120 ft/s. What is the height of the cliff?
**64.** If a diver of mass \( m \) stands at the end of a diving board with length \( L \) and linear density \( \rho \), then the board takes on the shape of a curve \( y = f(x) \), where
\[
EI y'' = mg
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