Cricket Ball Speed and Angle: Will It Go for a Six?

Question:

In the cricket game,a batsman strikes the ball such that it moves with a speed 30 ms^-1 at an angle 30^o with the horizontal. The boundary line of the cricket ground is located at a distance of 75 m from the batsman.Will the ball go for a six?(Neglect air resistance, take g=9.8 ms^-2)

Solution:

Projectile motion:

The motion of a cricket ball in air is essentially a projectile motion.

Range of a projectile:

The range (R) of the projectile is given by

$${R=\frac{u^2\sin 2\theta}{g}}$$

Where u is the initial speed of the cricket ball

and the angle of projection is 30^o

$${R=\frac{30^2 \sin (2)(30)}{9.8}}$$

$${R=\frac{900 \ \sin 60}{9.8}}$$

$${R=\frac{900(\frac{\sqrt3}{2})}{9.8}}$$

$${R=\frac{900(1.732)}{19.6}}$$

$${R= 79.5 \ m}$$

The distance (79.5 m) is greater than the distance of the boundary line (75 m).

The ball will cross the boundary line and go for a six.

Range of a projectile:

PROJECTILE MOTION QUIZ: