Your name is Galileo Galilei and you toss a weight upward at 8 feet per second from the top of the Leaning Tower of Pisa (height

Question

3 years ago

8

Your name is Galileo Galilei and you toss a weight upward at 8 feet per second from the top of the Leaning Tower of Pisa (height

185 ft).
(a) Neglecting air resistance, find the weight's velocity as a function of time t.
v(t) = ? ft/s
(b) Find the height (in feet) of the weight above the ground as a function of time.
s(t) = ?
Where and when will it reach its zenith?
? ft
? s

Physics

1 answer:

Llana [10] · Answer 1 · 2022-07-02T22:32:06+03:00

a) $v(t)=8 -32.2t$ [ft/s]

b) $h(t)=185+8t-16.1t^2$ [ft]

c) 186 ft at 0.248 s

Explanation:

a)

The motion of the weight is a free fall motion, which is subjected only to the force of gravity, downward.

Therefore, the motion of the object will be a uniformly accelerated motion, with constant acceleration of

$g=32.2 ft/s^2$ (acceleration due to gravity)

in the downward direction.

Therefore, the velocity of the weight after time t will be given by the following suvat equation:

$v(t)=u-gt$

where:

$u=+8 ft/s$ is the initial vertical velocity (upward)

t is the time

Substituting the values of u and g, we find

$v(t)=8 -32.2t$ [ft/s]

b)

Since the motion of the weight is a uniformly accelerated motion, the expression that gives the displacement of the object at time t (and therefore, its height at time t), is given by

$h(t)=h_0 + ut -\frac{1}{2}gt^2$

where

$h_0 = 185 ft$ is the initial height of the weight

$u=+8 ft/s$ is the initial vertical velocity (upward)

$g=32.2 ft/s^2$ (acceleration due to gravity)

t is the time

And substituting these values, we find:

$h(t)=185+8t-16.1t^2$ [ft]

c)

The time at which the weight reaches its maximum height above the ground can be found from the equation of the velocity: in fact, at the moment of maximum height, the direction of the weight changes, so its velocity will be zero at that instant:

$v(t)=0$