Question

A distance is calculated from the equation d gt2. g is exactly known to be 9.8014 m/s and t is measured to be 2.4 0.2 s. What is the distance and the uncertainty in the distance?

Answer 1

Explanation:

The distance covered by an object is given by the following equation as :

$d=\dfrac{1}{2}gt^2$..............(1)

Where

g is the acceleration due to gravity

t is the time

The value of t is measured to be, $t=(2.4\pm 0.2)\ s$

To find the distance covered, put the value of t = 2.4 s in equation (1).

$d=\dfrac{1}{2}\times 9.8\times (2.4)^2$

d = 28.224 meters

To find the uncertainty in the distance, put the value of t = 0.2 s in equation (1) as :

$d=\dfrac{1}{2}gt^2$

$d=\dfrac{1}{2}\times 9.8\times (0.2)^2$

d = 0.196 meters

Hence, this is the required solution.