A stone is thrown vertically upward from the ground level with a speed of 25m/s . At what time is it 5m above the ground?

Approximately and then approximately , assuming that air resistance on the stone is negligible and that .

Explanation:

Let denote the height of the stone.

Let denote the gravitational acceleration.

Let denote the initial velocity of the stone. In this question, .

Let denote the time (measured in seconds) after the stone was thrown.

The following SUVAT equation relates these quantities:

.

The value of height , gravitational acceleration , and initial velocity are all known: , , and . Substitute these values into the equation to obtain a quadratic equation about time (in seconds):

.

Simplify this equation to obtain:

.

Solve this equation using the quadratic formula. The two roots of this quadratic equation about are:

, and

.

Both roots are greater than and are valid.

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