Question

A stone projected at an angle just clean a wall $100$ m high at a distance of $200$m from the point of the projection. then the angle of projection is –
(A)${30^ \circ }$
(B)${45^ \circ }$
(C)${60^ \circ }$
(D)${75^ \circ }$

Answer 1

Hint: In this question we need to apply the concept of minimum angle of projection to find the required angle of projection, which is given by
tan$\theta $=$\dfrac{{vertical{\text{ }}height{\text{ }}of{\text{ }}the{\text{ }}projection}}{{horizontal{\text{ }}distance{\text{ }}of{\text{ }}projection}}$
then we need to consider the angle which is closest to the minimum angle found from the question.

Complete answer:
Projectile motion of a body is known as the motion of the object after being projected in the air and the motion governed by gravity. And the object in motion is known as projectile and the path followed by the object is known as trajectory.
The tangent of minimum angle of projection of any projectile is given by the ratio of height of projectile and distance of projectile.
Given data for the projectile motion is
The height of the projectile given = $100m$
The distance of the projectile given = $200m$
Now for calculating the angle of projection, $\theta $ we have to solve the following equation.
angle of projection = \[ta{n^{ - 1}}\]$\dfrac{{{\text{ }}height{\text{ }}of{\text{ }}the{\text{ }}projection}}{{{\text{ }}distance{\text{ }}of{\text{ }}projection}}$
angle of projection=$\theta = {\tan ^{ - 1}}\left( {\dfrac{{100}}{{200}}} \right)$
                                      $\theta = {26.6^ \circ }$
As the minimum angle of projection required is $\theta = {26.6^ \circ }$ to clear the wall if the ball is projected in a straight line thus as the ball is moving in a curved path or projectile thus we would require to project the ball at angle greater than $\theta = {26.6^ \circ }$so that the ball clears the wall hence the best possible angle of projection is ${30^ \circ }$.

Note:
Even though the answer and option do not match we will select ${30^ \circ }$ as our answer considering it to be the nearest to our answer.