Question

A ball is projected from a point on the floor with a speed of 15 m/s at an angle of 60° with the horizontal. Will it hit a vertical wall 5 m away from the point of projection and perpendicular to the plane of projection without hitting the floor ? Will the answer differ if the wall is 22 m away ?Concept of Physics - 1 , HC VERMA , Chapter "Rest and Motion : Kinematics

Answer 1

Solution :
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u=15m/s
θ=60°
g=9.8m/s2

Horizontal Range, x=u²sin2θ/g
x=15x15 sin120°/9.8
=225x√3/2x9.8
x=225x1.73/19.6
x=19.8m

So in the first case, the wall is 5m away from projection point so it is in the horizontal range of projectile. So the ball will hit the wall.

In the second case, (22m away ) wall is not within the horizontal range. So the ball would not hit the wall.

Answer 2

HEY!!

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▶Vertical velocity of the ball= 15 sin 60=7.5root3

▶Vertical velocity of the ball = 15 cos 60 = 7.5 

▶Time of flight=

2(vertical velocity)/g=15root3/ 10=3root3/2

▶Range= 3root3/2 × 7.5 = 19.485

✔Therefore, if the wall is 22 m away from the point of projection of ball, the ball will not hit the wall as it will fall at a distance of 19.485 m from the point of projection.