11. A ball is thrown vertically into the air with unknown ve- locity vo at time t = 0. Assume that the ball is thrown from about shoulder height, say yo = 1.5 m. If you ignore air resistance, then it is easy to show that dv/dt = -g, where g = 9.8 m/s² is the acceleration due to gravity. Follow the lead of exercise 7 to show that v dv = –g dy. Further, because the velocity of the ball is zero when it reaches its maximum height, %3D 15 dv= -g dy. 1.5 a) Find the initial velocity of the ball if the ball reaches a maximum height of 15 m. Next, let's include air resistance. Suppose that R(v) = -rv and show that the equation of motion be- comes v dv = (-8 – v) dy. c)If the mass of the ball is 0.1 kg and r = 0.02 N/(m/s), find the initial velocity if the ball is again released from shoul- der height (yo = 1.5 m) and reaches a maximum height of 15 m.
11. A ball is thrown vertically into the air with unknown ve- locity vo at time t = 0. Assume that the ball is thrown from about shoulder height, say yo = 1.5 m. If you ignore air resistance, then it is easy to show that dv/dt = -g, where g = 9.8 m/s² is the acceleration due to gravity. Follow the lead of exercise 7 to show that v dv = –g dy. Further, because the velocity of the ball is zero when it reaches its maximum height, %3D 15 dv= -g dy. 1.5 a) Find the initial velocity of the ball if the ball reaches a maximum height of 15 m. Next, let's include air resistance. Suppose that R(v) = -rv and show that the equation of motion be- comes v dv = (-8 – v) dy. c)If the mass of the ball is 0.1 kg and r = 0.02 N/(m/s), find the initial velocity if the ball is again released from shoul- der height (yo = 1.5 m) and reaches a maximum height of 15 m.
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Please see question attached in pic 1 and see the student solution in pic 2. Can you please show in steps how they arrive at the solutions?
Transcribed Image Text:11. Without air resistance, vo
16.2665m/s. With air resistance, vo is defined by
V2 x 13.5g
%3D
15
vdv
r
vo v+ mg/r
dy.
/1.5
т
Hence,
- vo + (mg/r) In(vo + mg/r) – (mg/r) In(mg/r)
= -13.5- or
m
- vo + 49 In(vo + 49) – 49 In(49) = -2.7
-
This is an implicit equation for vo. Solving on a
calculator or a computer yields vo = 18.1142m/s.
Transcribed Image Text:11. A ball is thrown vertically into the air with unknown ve-
locity vo at time t = 0. Assume that the ball is thrown
from about shoulder height, say yo = 1.5 m. If you ignore
air resistance, then it is easy to show that dv/dt = -g,
where g = 9.8 m/s² is the acceleration due to gravity.
Follow the lead of exercise 7 to show that v dv = –g dy.
Further, because the velocity of the ball is zero when it
reaches its maximum height,
15
v dv =
-g dy.
/1.5
a) Find the initial velocity of the ball if the ball reaches a
maximum height of 15 m.
Next, let's include air resistance. Suppose that
R(v) = -rv and show that the equation of motion be-
comes
v dv = (-8 – -v) dy.
m
c)If the mass of the ball is 0.1 kg and r = 0.02 N/(m/s), find
the initial velocity if the ball is again released from shoul-
der height (yo = 1.5 m) and reaches a maximum height of
15 m.
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