a boy is standing on a pole of height 14.7m throws a stone upwards. it moves in a vertical line slightly away from the pole and falls on the ground. its equation of motion in meters and seconds is x=9.8t-4.9t^2. find time taken for upward and downward motions. also find the maximum height reached by the stone from the ground.

The time taken for the upward motion is 1 second. The same time is taken for the downward motion

It reaches a maximum height of 4.9 meters.

Step-by-step explanation:

The equation of motion is:

Since the term which multiplies t squared is negative, the graph is concave down, that is, x increases until the vertex, where it reaches it's maximum height, then it decreases.

Vertex of a quadratic equation:

Quadratic equation in the format

The vertex is the point , in which

In this question:

So

Vertex:

The time taken for the upward motion is 1 second.

It reaches a maximum height of 4.9 meters.

Downward motion:

From the vertex to the ground.

The ground is t when x = 0. So

Or

It reaches the ground when t = 2 seconds.

The downward motion started at the vertex, when t = 1.

So the duration of the downward motion is 2 - 1 = 1 second.

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step-by-step explanation: