Question

our name is Galileo Galilei and you toss a weight upward at 20 feet per second from the top of the Leaning Tower of Pisa (height 184 ft). (a) Neglecting air resistance, find the weight's velocity as a function of time t. v(t) = 20−32t ft/s (b) Find the height (in feet) of the weight above the ground as a function of time. HINT [See Example 8.] s(t) = 184+20t−16t2 Where and when will it reach its zenith?? ft? s

Answer 1

Answer

given,

velocity of weight = 20 ft/s

height of the leaning tower = 184 ft

velocity of weight

acceleration due to gravity

g = 32 ft/s

a) using equation of motion

v = u + at

v(t) = 20 - g t

v(t) = 20 - 32 t   ft/s

b) $s (t) = s (0) + v (0) t +\dfrac{1}{2}at^2$

    $s (t) = 184 +20 t - \dfrac{1}{2}\times 32 t^2$

    $s (t) = 184 +20 t - 16 t^2$

at zenith v(t) is equal to zero

 v(t) = 20 -32 t

 0 = 20 - 32 t

  t = 0.625 s

height at instant t = 0.625 s

    $s (0.625) = 184 +20\times 0.625  - 16\times 0.625^2$

     s = 190.25 m

Answer 2

• The weight's velocity as a function of time t

Parameters

velocity of weight = 20 ft/s

height of the leaning tower = 184 ft

velocity of weight = ?

acceleration due to gravity = 32 ft/s

v = u + at

v(t) = 20 - g t

v(t) = 20 - 32 t ft/s.

• The height (in feet) of the weight above the ground

s(t) = s(0) + v (0)t + 1/2at²

     = 184 + 20t - 1/2 ˣ 32t²

     = 184 + 20t - 16t²

At the zenith, v(t) is equal to zero

v(t) = 20 -32 t

0 = 20 - 32 t

t = 0.625 s

S(0.625) = 184 +20 - 16 ˣ 0.625²

 s = 190.25 m.

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