An object falls from a height towards the ground under gravity. It takes 5 seconds to reach the ground. Given that the acceleration due to gravity $g = 10 m/s^2$, we need to find: (1) The maximum velocity gained by the object. (2) The height from which it fell.

1. Problem Description

An object falls from a height towards the ground under gravity. It takes 5 seconds to reach the ground. Given that the acceleration due to gravity $g = 10 m/s^2$, we need to find:

(1) The maximum velocity gained by the object.

(2) The height from which it fell.

2. Solution Steps

(1) Maximum Velocity:

The object starts with an initial velocity of 0 m/s and accelerates due to gravity. The final velocity $v$ after time $t$ can be calculated using the formula:

$v = u + at$, where $u$ is the initial velocity, $a$ is the acceleration, and $t$ is the time.

In this case, $u = 0 m/s$, $a = g = 10 m/s^2$, and $t = 5 s$.

So, $v = 0 + (10 m/s^2)(5 s) = 50 m/s$.

The maximum velocity gained by the object is 50 m/s.

(2) Height of the Fall:

The height $h$ from which the object fell can be calculated using the formula:

$h = ut + \frac{1}{2}at^2$

Since $u = 0 m/s$, $a = g = 10 m/s^2$, and $t = 5 s$:

$h = (0)(5) + \frac{1}{2}(10)(5^2) = 0 + \frac{1}{2}(10)(25) = 5(25) = 125 m$.

The height from which the object fell is 125 m.

3. Final Answer

(1) The maximum velocity gained by the object is 50 m/s.

(2) The height from which the object fell is 125 m.