A pair of glasses is dropped from the top of a 32.0m stadium. A pen is dropped 2.Os later. How high above the ground is the pen when the spectacles hit the ground? Neglect the air resistance.

The pen is 30.52 m above the ground.

Given that the height of the stadium is h = 32m

The initial velocity of the glasses will be 0.

is the time taken for the glasses to hit the ground.

Now the pen is released 2 seconds later. So by the time the glasses hit the ground the pen has spent:

in the air

distance traveled by the pen:

So the pen is    above the ground.

Learn More:

link

Explanation:

Free Fall Motion

A free-falling object refers to an object that is falling under the sole influence of gravity. If the object is dropped from a certain height h, it moves downwards until it reaches ground level.

The speed vf of the object when a time t has passed is given by:

Where

Similarly, the distance y the object has traveled is calculated as follows:

If we know the height h from which the object was dropped, we can solve the above equation for t:

The stadium is h=32 m high. A pair of glasses is dropped from the top and reaches the ground at a time:

The pen is dropped 2 seconds after the glasses. When the glasses hit the ground, the pen has been falling for:

Therefore, it has traveled down a distance:

Thus, the height of the pen is: