A potato is launched vertically upward with an initial velocity of 170 feet per second from a potato gun at the top of a 66-foot-tall building. The distance in feet that the potato travels from the ground after *t* seconds is given by \( s(t) = -16t^2 + 170t + 66 \).**a) Find the velocity of the potato after 2.2 seconds and 7 seconds.**- At \( t = 2.2 \) seconds, \( v = \) _____ feet per second.- At \( t = 7 \) seconds, \( v = \) _____ feet per second.**b) Find the speed of the potato at 2.2 seconds and 7 seconds.**- At \( t = 2.2 \) seconds, the speed of the potato is _____ feet per second.- At \( t = 7 \) seconds, the speed of the potato is _____ feet per second.**c) Determine when the potato reaches its maximum height.**- \( t = \) _____ seconds**d) Find the acceleration of the potato at 2.2 seconds and 7 seconds.**- At \( t = 2.2 \) seconds, \( a = \) _____ feet per second per second.- At \( t = 7 \) seconds, \( a = \) _____ feet per second per second.**Determine how long the potato is in the air.**- _____ seconds**Determine the velocity of the potato upon hitting the ground.**- _____ feet per secondThere are no graphs or diagrams in this text.

Solution: (a) s = -16t2 + 170t + 66 Velocity is given by, v = ds/dt = 170 - 32t…

A potato is launched vertically upward with an initial velocity of 170 feet per second from a potato gun at the top of an 66-foot-tall building. The distance in feet that the potato travels from the ground after t seconds is given by s(t) 16+2 + 170t + 66. a) Find the velocity of the potato after 2.2 seconds and 7 seconds. At t = 2.2 seconds, v = At t = 7 seconds, v = feet per second. feet per second. b) Find the speed of the potato at 2.2 second and 7 seconds. At t = 2.2 seconds, the speed of the potato is At t = 7 seconds, the speed of the potato is c) Determine when the potato reaches its maximum height. t seconds Determine how long the potato is in the air. seconds. d) Find the acceleration of the potato at 2.2 seconds and 7 seconds. At t = 2.2 seconds, a = At t = 7 seconds, a = feet per second. Determine the velocity of the potato upon hitting the ground. feet per second. feet per second. feet per second per second. feet per second per second.

A potato is launched vertically upward with an initial velocity of 170 feet per second from a potato gun at the top of an 66-foot-tall building. The distance in feet that the potato travels from the ground after t seconds is given by s(t) 16+2 + 170t + 66. a) Find the velocity of the potato after 2.2 seconds and 7 seconds. At t = 2.2 seconds, v = At t = 7 seconds, v = feet per second. feet per second. b) Find the speed of the potato at 2.2 second and 7 seconds. At t = 2.2 seconds, the speed of the potato is At t = 7 seconds, the speed of the potato is c) Determine when the potato reaches its maximum height. t seconds Determine how long the potato is in the air. seconds. d) Find the acceleration of the potato at 2.2 seconds and 7 seconds. At t = 2.2 seconds, a = At t = 7 seconds, a = feet per second. Determine the velocity of the potato upon hitting the ground. feet per second. feet per second. feet per second per second. feet per second per second.

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

A potato is launched vertically upward with an initial velocity of 170 feet per second from a potato gun at the top of a 66-foot-tall building. The distance in feet that the potato travels from the ground after *t* seconds is given by \( s(t) = -16t^2 + 170t + 66 \).

**a) Find the velocity of the potato after 2.2 seconds and 7 seconds.**

- At \( t = 2.2 \) seconds, \( v = \) _____ feet per second.
- At \( t = 7 \) seconds, \( v = \) _____ feet per second.

**b) Find the speed of the potato at 2.2 seconds and 7 seconds.**

- At \( t = 2.2 \) seconds, the speed of the potato is _____ feet per second.
- At \( t = 7 \) seconds, the speed of the potato is _____ feet per second.

**c) Determine when the potato reaches its maximum height.**

- \( t = \) _____ seconds

**d) Find the acceleration of the potato at 2.2 seconds and 7 seconds.**

- At \( t = 2.2 \) seconds, \( a = \) _____ feet per second per second.
- At \( t = 7 \) seconds, \( a = \) _____ feet per second per second.

**Determine how long the potato is in the air.**

- _____ seconds

**Determine the velocity of the potato upon hitting the ground.**

- _____ feet per second

There are no graphs or diagrams in this text.

Expert Solution

Step 1

Solution:

(a) s = -16t²+ 170t + 66

Velocity is given by,

v = ds/dt = 170 - 32t

So, at t = 2.2 seconds, velocity is (170 - 32x2.2) = 99.6 ft/sec upwards. [Ans]

At t = 7 seconds, velocity is (170 - 32x7) = -54 ft/sec, i.e., 54 ft/sec downwards. [Ans]

(b) distance travelled in t = 2.2 seconds is (-16x2.2² + 170x2.2 + 66) = 362.56 ft

So, speed at t = 2.2 seconds is 362.56/2.2 = 164.8 ft/sec. [Ans]

distance travelled in t = 7 seconds is (-16x7² + 170x7 + 66) = 472 ft.

So, speed at t = 7 seconds is 472/7 ≈67.43 ft/sec. [Ans]

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