Question

How can we find out how long it takes an object to reach its maximum height after being thrown up?

Answer 1

To determine the time it takes for an object to reach its maximum height after being thrown upward, we can use the concept of projectile motion. The key factor in this scenario is the vertical component of the object's velocity.

When an object is thrown vertically upward, its initial velocity in the upward direction decreases due to the force of gravity until it reaches its maximum height. At the maximum height, the object momentarily comes to a stop before falling back down.

The time it takes for the object to reach its maximum height can be found using the following equation:

$v_f=v_i+at$,

where:

• $v_f$ is the final velocity (which is zero at the maximum height),
• $v_i$ is the initial velocity (the velocity at the moment of release),
• $a$ is the acceleration (acceleration due to gravity, which is approximately $9.8{\text{m/s}}^2$ directed downward), and
• $t$ is the time.

Since the object reaches a stop at its maximum height, the final velocity is zero. Rearranging the equation, we have:

$0=v_i-9.8t$.

Simplifying further, we get:

$v_i=9.8t$.

Now, we can solve for $t$ by rearranging the equation:

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