Question

acceleration and gravity, part 1
the earths force of gravity creates an acceleration of 9.8 m/sec/sec on a freely falling body.
using the equation , ( a = \frac { v _ { f } - v _ { i } } { t } ), we can therefore calculate the velocity of a falling object at
any time if the initial velocity is known.
example: what is the velocity of a rubber ball dropped
from a building roof after 5 seconds?
answer: ( 9.8 mathrm { m } / mathrm { sec } / mathrm { sec } = \frac { v _ { f } - 0 } { 5 mathrm { sec } } )
( v _ { f } = 49 mathrm { m } / mathrm { sec } )
provide the answers to the questions below.

1. what velocity would a ball dropped from a tower have after after 10 seconds?

answer:

1. if a piece of wood dropped from a tall building has reached a velocity of 68.6 m/s, for how long has it been falling?

answer:

1. if a freely falling object currently has a velocity of 19.6 m/s, what is its velocity four seconds later?

answer:

1. if a piece of stone has attained a velocity of 88.2 m/sec after falling for 8 seconds, what was its initial velocity?

answer:

1. if an object is dropped, how long will it take to attain a velocity of 127.4 m/sec?

answer:

Explanation:

Step1: Identify the formula

The formula for acceleration is \(a=\frac{v_{f}-v_{i}}{t}\), where \(a = 9.8m/s^{2}\) (acceleration due to gravity), \(v_{i}\) is the initial velocity, \(v_{f}\) is the final velocity, and \(t\) is the time. When an object is dropped, \(v_{i}=0m/s\).

Step2: Solve question 1

Given \(a = 9.8m/s^{2}\), \(v_{i}=0m/s\), \(t = 10s\).
Substitute into the formula \(a=\frac{v_{f}-v_{i}}{t}\), we get \(9.8=\frac{v_{f}-0}{10}\).
Multiply both sides by \(10\): \(v_{f}=9.8\times10 = 98m/s\).

Step3: Solve question 2

Given \(a = 9.8m/s^{2}\), \(v_{i}=0m/s\), \(v_{f}=68.6m/s\).
Substitute into \(a=\frac{v_{f}-v_{i}}{t}\), we get \(9.8=\frac{68.6 - 0}{t}\).
Solve for \(t\): \(t=\frac{68.6}{9.8}=7s\).

Step4: Solve question 3

Given \(a = 9.8m/s^{2}\), \(v_{i}=19.6m/s\), \(t = 4s\).
Substitute into \(a=\frac{v_{f}-v_{i}}{t}\), we get \(9.8=\frac{v_{f}-19.6}{4}\).
Multiply both sides by \(4\): \(39.2=v_{f}-19.6\).
Add \(19.6\) to both sides: \(v_{f}=39.2 + 19.6=58.8m/s\).

Step5: Solve question 4

Given \(a = 9.8m/s^{2}\), \(v_{f}=88.2m/s\), \(t = 8s\).
Substitute into \(a=\frac{v_{f}-v_{i}}{t}\), we get \(9.8=\frac{88.2-v_{i}}{8}\).
Multiply both sides by \(8\): \(78.4=88.2 - v_{i}\).
Solve for \(v_{i}\): \(v_{i}=88.2-78.4 = 9.8m/s\).

Step6: Solve question 5

Given \(a = 9.8m/s^{2}\), \(v_{i}=0m/s\), \(v_{f}=127.4m/s\).
Substitute into \(a=\frac{v_{f}-v_{i}}{t}\), we get \(9.8=\frac{127.4-0}{t}\).
Solve for \(t\): \(t=\frac{127.4}{9.8}=13s\).

Answer:

1. \(98m/s\)
2. \(7s\)
3. \(58.8m/s\)
4. \(9.8m/s\)
5. \(13s\)