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# A body is thrown with a velocity of 9.8m/s making an angle of ${30^ \circ }$ with the horizontal. It will hit the ground after a time:A) 1.5 sB) 1 sC) 3 s D) 2 s

Last updated date: 18th Sep 2024
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Hint: The motion of an object thrown or projected into the air, which is a subject to only the acceleration of gravity is known as projectile motion. The object is called a projectile, and the path covered by the object or projectile is called its trajectory.

Formula Used: The numerical formula to calculate the time of flight of a projectile is given by the mathematical expression given below:
$T = \dfrac{{2 \times {u_y}}}{g}$
In this mathematical equation to calculate the time of flight of a projectile, ${u_y}$ is the vertical velocity of the projectile or the velocity of the projectile along the direction of the y-axis.
$g$ is the acceleration due to gravity which is numerically equal to $9.8m{s^{ - 2}}$.

One of the most important things illustrated by projectile motion is that vertical and horizontal motions are independent of each other. Galileo was the first person to fully comprehend this characteristic. He used it to predict the range of a projectile.
In this question we have to take into consideration the velocity of the projectile along the y-axis or the vertical velocity of the object or projectile. Thus, we have:
${u_y} = u\sin \theta$
Now we substitute this equation in the mathematical formula to obtain the final expression for time of flight. Thus:
$T = \dfrac{{2 \times u\sin \theta }}{g}$
Now, we know that from the data given in the numerical problem.
$u = 9.8m/s$, $\theta = 3{0^ \circ }$ and $g = 9.8m{s^{ - 2}}$
Thus, substituting these values in the above mathematical equation, we get:
$T = \dfrac{{2 \times 9.8 \times \sin 30^\circ }}{{9.8}}$
Solving this equation further, we obtain:
$\Rightarrow T = 2 \times \dfrac{1}{2} = 1s$

Thus the projectile takes one second to hit the ground.

Note: Note that this definition assumes that the upwards direction is defined as the positive direction. If we arrange the coordinate system instead such that the downwards direction is positive, then acceleration due to gravity takes a positive value.