### Video Transcript

A body was projected vertically upwards at 9.1 meters per second. Determine the time taken to reach the maximum height. Take ๐ equal to 9.8 metres per second squared.

In order to solve this question, we will use one of the equations of motion or SUVAT equations: ๐ฃ equals ๐ข plus ๐๐ก, where ๐ข is the initial velocity, ๐ฃ is the final velocity, ๐ is the acceleration, and ๐ก is equal to the time. The body is projected vertically upwards at 9.1 meters per second. This means that ๐ข is equal to 9.1. At the maximum height, the velocity of the body is zero metres per second. Therefore, ๐ฃ is equal to zero. As gravity is working against the body, ๐ is equal to negative 9.8 metres per second squared. And finally, ๐ก is the value weโre trying to calculate.

Substituting in these values into the equation ๐ฃ equals ๐ข plus ๐๐ก gives us zero is equal to 9.1 minus 9.8๐ก. Rearranging this equation gives us 9.8๐ก is equal to 9.1. Dividing both sides of the equation by 9.8 gives us a value for ๐ก of 9.1 divided by 9.8. This is equal to 13 14ths of a second or 0.93 seconds to two decimal places.

This means that the time taken for a body to reach its maximum height if it is projected vertically upwards at 9.1 meters per second is 13 14ths of a second.