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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

A stone is dropped from the upper observation deck (the Space Deck) of the CN Tower, 450 m above the ground.

(a) Find the distance of the stone above ground level at time t.

(b) How long does it take the stone to reach the ground?

(c) With what velocity does it strike the ground?

(d) If the stone is thrown downward with a speed of 5 m/s, how long does it take to reach the ground?

(a)

To determine

To find: The distance of stone above the ground level.

Explanation

Given data:

The distance between upper observation deck and ground is 450 m.

Formula used:

Write the expression for acceleration function a(t) .

a(t)=v(t) (1)

Here,

v(t) is first derivative of velocity function v(t) .

Write the expression for velocity function v(t) .

v(t)=s(t) (2)

Here,

s(t) is first derivative of position function s(t) .

Antiderivative of t3 is 14t4 , t2 is 13t3 , t is 12t2 and 1 is t .

Calculation:

At first observation, velocity is zero and position is at 450 m at t=0 , as the stone is dropped 450 m height to ground level. Hence,

v(0)=0s(0)=450

The motion of stone is close to ground, so the motion is considered as gravitational constant (g) , which is 9.8ms2 .

Write the expression for acceleration function (a(t)) .

a(t)=9.8

Substitute 9.8 for a(t) in equation (1),

v(t)=9.8

Antiderivate the expression with respect to t,

v(t)=9

(b)

To determine

To find: The time that stone takes to reach ground.

(c)

To determine

To find: The velocity that stone strikes the ground.

(d)

To determine

To find: The time that stone takes to reach ground.

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