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Question: A stone projected at an angle just clean a wall \(100\) m high at a distance of \(200\)m from the po...

A stone projected at an angle just clean a wall 100100 m high at a distance of 200200m from the point of the projection. then the angle of projection is –
(A)30∘{30^ \circ }
(B)45∘{45^ \circ }
(C)60∘{60^ \circ }
(D)75∘{75^ \circ }

Explanation

Solution

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
tanθ\theta =vertical height of the projectionhorizontal distance of projection\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 = 100m100m
The distance of the projectile given = 200m200m
Now for calculating the angle of projection, θ\theta we have to solve the following equation.
angle of projection = tan−1ta{n^{ - 1}}$\dfrac{{{\text{ }}height{\text{ }}of{\text{ }}the{\text{ }}projection}}{{{\text{ }}distance{\text{ }}of{\text{ }}projection}}angleofprojection= angle of projection=\theta = {\tan ^{ - 1}}\left( {\dfrac{{100}}{{200}}} \right) \theta = {26.6^ \circ }Astheminimumangleofprojectionrequiredis As the minimum angle of projection required is\theta = {26.6^ \circ }toclearthewalliftheballisprojectedinastraightlinethusastheballismovinginacurvedpathorprojectilethuswewouldrequiretoprojecttheballatanglegreaterthanto clear the wall if the ball is projected in a straight line thus as the ball is moving in a curved path or projectile thus we would require to project the ball at angle greater than\theta = {26.6^ \circ }sothattheballclearsthewallhencethebestpossibleangleofprojectionisso that the ball clears the wall hence the best possible angle of projection is {30^ \circ }$.

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