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

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/sΒ².

01:51

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 𝑒 plus π‘Žπ‘‘, where 𝑒 is the initial velocity, 𝑣 is the final velocity, π‘Ž is the acceleration, and 𝑑 is equal to the time. The body is projected vertically upwards at 9.1 meters per second. This means that 𝑒 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, π‘Ž is equal to negative 9.8 metres per second squared. And finally, 𝑑 is the value we’re trying to calculate.

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

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.