Question

How can we calculate the time taken to reach maximum height if we know the object's initial velocity?

Answer 1

To calculate the time taken to reach the maximum height of an object, given its initial velocity, you can use the following steps:

1. Identify the initial vertical velocity (Vy) of the object. This velocity is the vertical component of the initial velocity.

2. Determine the acceleration due to gravity (g), which is approximately 9.8 m/s² near the Earth's surface.

3. Use the equation for vertical motion under constant acceleration:

   Δy = Vy * t + (1/2) * g * t²

   Where:

   • Δy is the displacement in the vertical direction (in this case, the maximum height),
   • Vy is the initial vertical velocity,
   • g is the acceleration due to gravity,
   • t is the time taken to reach the maximum height.

4. At the maximum height, the object's vertical displacement is zero because it momentarily comes to rest before falling back down. Thus, you can set Δy to zero:

   0 = Vy * t + (1/2) * g * t²

5. Rearrange the equation to solve for the time (t):

   (1/2) * g * t² = - Vy * t

   Divide both sides by t:

   (1/2) * g * t = -Vy

   Divide both sides by (1/2) * g:

   t = -2 * Vy / g

   Note: The negative sign arises because the initial vertical velocity is typically considered positive when upward.

By following these steps and plugging in the values of the initial vertical velocity (Vy) and the acceleration due to gravity (g), you can calculate the time taken to reach the maximum height.