Question

A stone thrown vertically upward direction with velocity of 12m/s, does it take a certain time to reach the maximum height?

Answer 1

Yes, the stone thrown vertically upward with a velocity of 12 m/s will take a certain amount of time to reach its maximum height.

When an object is thrown vertically upwards, it experiences a constant acceleration due to gravity, which acts in the downward direction. This acceleration is usually denoted as "g" and has a magnitude of approximately 9.8 m/s² near the surface of the Earth.

As the stone moves upward, its velocity decreases due to the opposing acceleration of gravity. At the highest point of its trajectory, the stone momentarily comes to rest before reversing its direction and falling back down. This highest point is called the maximum height.

To determine the time taken to reach the maximum height, we need to consider the initial velocity, final velocity, and the acceleration of the stone.

The final velocity at the maximum height is zero since the stone momentarily comes to rest. The initial velocity is given as 12 m/s, and the acceleration due to gravity is -9.8 m/s² (negative because it acts in the opposite direction to the upward motion).

Using the kinematic equation:

$v_f=v_i+at$

Where: v_f = final velocity (0 m/s), v_i = initial velocity (12 m/s), a = acceleration (-9.8 m/s²), t = time taken.

Plugging in the values:

$0=12-9.8t$

Solving for "t":

$9.8t=12$

$t=\frac{12}{9.8}\approx 1.22\text{ seconds}$

Therefore, it takes approximately 1.22 seconds for the stone to reach its maximum height.