Question Video: Studying the Motion of an Upward Projected Body until It Comes Back to the Same Point | Nagwa Question Video: Studying the Motion of an Upward Projected Body until It Comes Back to the Same Point | Nagwa

# Question Video: Studying the Motion of an Upward Projected Body until It Comes Back to the Same Point Mathematics • Second Year of Secondary School

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A body was projected vertically upwards from the ground, and it took 157 seconds to return to the ground. Find the time π‘β for which the body was ascending and time π‘β for which it was descending.

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### Video Transcript

A body was projected vertically upwards from the ground, and it took 157 seconds to return to the ground. Find the time π‘ one for which the body was ascending and time π‘ two for which it was descending.

Our initial thoughts when dealing with a problem like this might be to use our equations of motion or SUVAT equations. These are π£ is equal to π’ plus ππ‘. π£ squared is equal to π’ squared plus two ππ . π  is equal to π’ plus π£ divided by two multiplied by π‘. π  is equal to π’π‘ plus a half ππ‘ squared. And π  is equal to π£π‘ minus a half ππ‘ squared. In all of these equations, π’ is equal to the initial velocity, π£ is the final velocity, π is the acceleration, π‘ is the time, and π  is the displacement.

This question, however, doesnβt require any of these formulas. This is because when we model a body as a particle and ignore air resistance, the time that it is ascending will be equal to the time it is descending. This means that π‘ one is equal to π‘ two. As the total time was 157 seconds, π‘ one plus π‘ two is equal to 157. Replacing π‘ two with π‘ one in this equation gives us two π‘ one is equal to 157. Dividing both sides of this equation by two gives us π‘ one is equal to 78.5. As π‘ one is equal to π‘ two, we can conclude that they are both equal to 78.5. The time for which the body is ascending and the time for which it was descending are both 78.5 seconds.

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