# Question #c8ae1

##### 1 Answer

**!! LONG ANSWER !!**

Initial velocity :

Maximum height:

Landing speed:

#### Explanation:

So, you know that the cork is launched from an initial height of **1.2 m**, and that it takes **2 seconds** until it lands **5 m** away from its initial position.

The fact that it doesn't fall in the exact same place from which it was launched tells you that it was launched at an *angle*, let's say

The initial velocity of the cork will thus have two components, a *vertical* one and a *horizontal* one.

In order to determine the angle of launch, you're going to have to use two equations, one tha describes the cork's *horizontal* motion and one that describes its *vertical* motion.

**Horizontally**, the cork moves without being acted upon by exterior forces. This means that you can use the *horizontal displacement* and total time of travel to write the *vertical component* of the initial velocity.

**Vertically**, things are a little more complicated. This time, the cork is acted upon by the force of gravity, which implies that the *vertical component* of its initial velocity will be affected by the *gravitational acceleration*,

Because the cork is launched from a height of **1.2 m**, but ends up at ground level, the *total vertical displacement* will be equal to **-1.2 m**.

Think of it like this: if the 1.2-m height is set as the zero level, then the cork ends up 1.2 m **lower** than that, hence the negative sign.

This means that you can write

So, you have two equations with two unknowns

Divide the bottom one by the top one to get

This means that the initial velocity was

To get the maximum height of the cork, use the fact that, *at the peak of its trajectory*, right before it starts to drop towards the ground, the *horizontal component* of its velocity will be equal to **zero**.

The cork takes **0.94 seconds** to reach the peak of its trajectory, which implies that it falls for

The height it reaches right before starting to drop will be

To get the final velocity of the cork, use the time it takes for the cork to drop to determine the *vertical component* of its final velocity. Once again, the fact that the vertical component of its velocity is **zero** at maximum height will come to your aid.

The *horizontal component* of its final velocity will be equal to that of the initial velocity. Finally, use Pythagoras' theorem to determine the final velocity