Question

a ball player in outfield has to judge a catch which he can knows he can get with equal ease at any height from the ground between 0.9m and 2.1m. what is the minimum and maximum distance he should have to be from the home plate? assume that the ball is given an initial speed of 34m/s and the maximum height of the ball 3.7m.

Answer 1

As per the given question,

Ball is at the height (h)=3.7m

Initial speed of the ball (u)= 34 m/sec

time taken by the ball to reach on the ground $h=ut+\frac{gt^2}{2}$

substituting the values,

$3.7= 34t +4.9t^2$

$4.9t^2+34t-3.7=0$

$t=\frac{-34\pm\sqrt{34^2+4\times 3.7\times4.9}}{2\times 4.9}=\frac{-34\pm 34.28}{9.8}$

Hence, $t=\frac{0.28}{9.8}=0.28sec$