# 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 π = 9.8 m/sΒ².

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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 π 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: π£ equals π’ plus ππ‘, where π’ is the initial velocity, π£ is the final velocity, π is the acceleration, and π‘ is equal to the time. The body is projected vertically upwards at 9.1 meters per second. This means that π’ is equal to 9.1. At the maximum height, the velocity of the body is zero metres per second. Therefore, π£ is equal to zero. As gravity is working against the body, π is equal to negative 9.8 metres per second squared. And finally, π‘ is the value weβre trying to calculate.

Substituting in these values into the equation π£ equals π’ plus ππ‘ gives us zero is equal to 9.1 minus 9.8π‘. Rearranging this equation gives us 9.8π‘ is equal to 9.1. Dividing both sides of the equation by 9.8 gives us a value for π‘ 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.