# Question Video: Finding the Time Taken by a Body to Reach the Maximum Height under Gravity given Its Initial Velocity Mathematics

A body was projected vertically upwards at 9.1 m/s. Determine the time taken to reach the maximum height, take 𝑔 = 9.8 m/s².

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### Video Transcript

A body was projected vertically upwards at 9.1 meters per second. Determine the time taken to reach the maximum height. Take 𝑔 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: 𝑣 equals 𝑢 plus 𝑎𝑡, where 𝑢 is the initial velocity, 𝑣 is the final velocity, 𝑎 is the acceleration, and 𝑡 is equal to the time. The body is projected vertically upwards at 9.1 meters per second. This means that 𝑢 is equal to 9.1. At the maximum height, the velocity of the body is zero metres per second. Therefore, 𝑣 is equal to zero. As gravity is working against the body, 𝑎 is equal to negative 9.8 metres per second squared. And finally, 𝑡 is the value we’re trying to calculate.

Substituting in these values into the equation 𝑣 equals 𝑢 plus 𝑎𝑡 gives us zero is equal to 9.1 minus 9.8𝑡. Rearranging this equation gives us 9.8𝑡 is equal to 9.1. Dividing both sides of the equation by 9.8 gives us a value for 𝑡 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.