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Chapter 3: Q12E (page 116)

A shell of mass 2 kg is shot upward with an initial velocity of 200 m/sec. The magnitude of the force on the shell due to air resistance is |v|/20. When will the shell reach its maximum height above the ground? What is the maximum height

Short Answer

Expert verified
  • The shell will reach at the maximum height in 16.48 seconds
  • The maximum height is 1534.8 m

Step by step solution

01

Find the velocity equation

Applying the formula for velocityv(t)=mgb+(vo-mgb)e-btm .

v(t)=3.92.4-592.4e-0.025t (where vo= -200 ,m = 2, b = 1/20 ,g = 9.81)

The shell reached at the maximum height when v(t)=0 then

role="math" localid="1663929004353" 0=3.92.4-592.4e-0.025te-0.025t=392.4592.4e-0.025t=0.66239t=16.48sec

Hence, the shell will reach at the maximum height in 16.48 seconds

02

Find the equation of motion

Apply formula for value equation of motion x(t)=mgtb+mb(vo-mgb)(1-e-btm)

x(t)=392.4t-23696(1-e-0.025t)

The maximum height at t = 16.48 sec then

x(t)=-1534.81m

Hence, the maximum height is 1534.8 m

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