**Problem 9:** The maximum height gained by a projectile
is 300 m. If it travels a range of 800 m, find the displacement of summit point
from the point of projection.

**Solution**

The trajectory of the projectile can be depicted as in following diagram.

ADC is the trajectory of the projectile with D as the highest point and AC as the range of the projectile. Now, AC = 800 m, DB = 300 m and AB = 400 m. Apply Pythagorean theorem to the right triangle,

(AD)^{2} =
(AB)^{2} + (BD)^{2}

Put the values,

(AD)^{2} =
(400)^{2} + (300)^{2}

(AD)^{2} =
160000 + 90000 = 250000

AD = √ 250000 = 500 m

This is the displacement of the summit (highest point) from the point of projection (A).

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