Question

Assertion (A): A projectile is projected at an angle θ and then at an angle (90° - θ), keeping the initial velocity same. In both the cases, the range will be same. Reason (R): Range of a projectile R = u2sin2θ

When the football travels through the air, it always follows a parabolic path because the movement of the ball in the vertical direction is influenced by the force of gravity. As the ball travels up, gravity slows it down until it stops for a moment at its peak height; the ball then comes down and gravity accelerates it until it hits the ground. When a footballer kicks a ball he has to consider 3 factors: • The velocity at which the ball leaves his feet • The angle of kick • The rotation of the ball The rotation of the ball determines how the ball will slow down in flight. The velocity of the ball and the angle of the kick are the major factors those determine: • How long the ball will remain in air (hangtime) • How high the ball will go • How far will the ball go When the ball leaves the footballer's foot, it moves in two directions - horizontally and vertically. If the ball is kicked at a steep angle, then it will have more velocity in the vertical direction than in the horizontal direction - the ball will go high, have a long hang-time, but travel a short distance. If the ball is kicked at a shallow angle, it will have more velocity in the horizontal direction than in the vertical direction - the ball will not go very high, will have a short hang-time, but will travel a long distance. The footballer decides on the best angle in view of his field position. A footballer kicks a ball with velocity 60 m/s at an angle a. For which of the following values of a, the hang-time will be highest?