Question

Kyle, a 100.0 kg football player, leaps straight up into the air (with no horizontal velocity) to catch a pass. He catches the 0.430 kg ball precisely at the peak of his jump, when he is 0.386 meters off the ground. He hits the ground 0.0295 meters away from where he leapt. If the ball was moving horizontally when it was caught, how fast was the ball traveling? ball's speed: m/s

Answer 1

here,

the mass of football player , m1 = 100 kg

the mass of ball , m2 = 0.43 kg

h = 0.386 m

let the tme taken to reach the ground be t

using second equation of motion

h = 0 + 0.5 * g * t^2

0.386 = 0 + 0.5 * 9.81 * t^2

solving for t

t = 0.281 s

x = 0.0295 m

the velocity after he catches the ball , v = x /t

v = 0.0295 /0.281 m/s = 0.105 m/s

let the initial velocity of the ball be u

using conservation of momentum

m2 * u = (m1 + m2) * v

0.43 * u = ( 100 + 0.43) * 0.105

solving for u

u = 24.56 m/s

the initial velocity of the ball is 24.56 m/s