an object is launched vertically in the air at 29.4 meters per second from 10 meter tall platform . find its maximum height in seconds and in meters ?
To find the maximum height reached by the object, we need to consider the motion of the object in terms of velocity and acceleration.
Step 1: Determine the initial velocity (u), final velocity (v), and acceleration (a) of the object.
Given:
Initial velocity, u = 29.4 m/s (upwards)
Acceleration, a = -9.8 m/s² (due to gravity, acting downwards)
Step 2: Find the time taken (t) for the object to reach its maximum height.
To find the time taken, we can use the following kinematic equation:
v = u + at
At the maximum height, the final velocity (v) is zero. Therefore:
0 = 29.4 - 9.8t
Simplifying the equation, we find:
9.8t = 29.4
t = 29.4 / 9.8
t ≈ 3 seconds
Therefore, it takes approximately 3 seconds for the object to reach its maximum height.
Step 3: Calculate the maximum height (h) reached by the object.
We can use the following equation of vertical motion:
h = ut + (1/2)at²
Plugging in the given values:
h = 29.4 * 3 + (1/2) * (-9.8) * (3)²
Simplifying the equation, we find:
h ≈ 44.1 - 44.1
h ≈ 44.1 meters
Therefore, the maximum height reached by the object is approximately 44.1 meters.