# Mixture of vectors and calculus

**Calculus**Level 3

A projectile is fired from origin with the velocity.. of \[\sqrt{5}ms^{-1}\] by making an angle of \(45^\circ\) with the positive direction of x-axis.

The area enclosed by the trajectory of projectile and x axis can be written as \(\frac{1}{a}\)

Find out the value of **a**

**Details and assumptions:-**
1.All the motions are along XY plane

2.Take \(g=10\text{ms}^{-2}\)

3.There is no other force except gravity acting on projectile

4.Gravitational force is acting on projectile along the negetive direction of y axis

5.Assume that x axis is working like ground