In a game of angry birds you launch a bird with an angle of 53 degrees to horizontal. Unfortunatly, its not a good shot and the bird flies through the air, missing all the targets, and lands on the ground. (same height from which it is launched) if its intial velocity was 10m/s, find the max height the bird can reach the horizontal displaccment total time bird is in the air

The maximum height covered is 3.25 m.

The horizontal distance covered is 9.81 m.

The total time in the air is 1.63 seconds.

Explanation:

The launch speed, .

Angle of launch with the horizontal,

So, the vertical component of the initial velocity,

.

The horizontal component of the initial velocity,

Let, t be the time of flight, to the horizontal distance covered

.

Not, applying the equation of motion in the vertical direction.

Where s is the displacement in time t, u is the initial velocity and a is the acceleration.

In this case, (from equation (i), s=0 (as the final height is same as the launch height) and (negative sign is due to the downward direction).

seconds.

So, the total time in the air is 1.63 seconds.

From equation (i),

Total horizontal distance covered is

.

Now, for the maximum height, H, applying the equation of motion as

Here, v is the final velocity and v=0 (at the maximum height), and h=H.

So,

.

Hence, the maximum height covered is 3.25 m.

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