A batter hits a fly ball which leaves the bat 1.0 m above the ground at an angle

Question

A batter hits a fly ball which leaves the bat 1.0 m above the ground at an angle of 60 with an initial speed of 28 m/s heading toward centerfield. Ignore air resistance.

Part A

How far from home plate would the ball land if not caught?

Express your answer using two significant figures.

Part B

The ball is caught by the centerfielder who, starting at a distance of 103 m from home plate, runs straight toward home plate at a constant speed and makes the catch at ground level. Find his speed.

Express your answer using two significant figures.

Explanation / Answer

here ,

initial speed , u = 28 m/s

theta = 60 degree

A)

let the distance is d

using equation of trajectory of projectile

y = x * tan(theta) - g * x^2/(2 * (v* cos(theta))^2) + y0

0 =1 + x * tan(60) - 9.8 * x^2/(2 * (28 * cos(60))^2)

solving for x

x = 69.9 m

the distance is 69.9 m

B)

time of flight is t

t =2 * v * sin(theta)/g

t = 2 * 28 * sin(60)/9.8

t = 4.95 s

Now , speed of fielder = (129 - 69.9)/4.95

speed of fielder = 11.94 m/s

the speed of centrefielder is 11.94 m/s

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