8. Golfer A hits golf ball A at an angle of 60 degree above the horizontal on th

Question

8. Golfer A hits golf ball A at an angle of 60 degree above the horizontal on the Moon, and the golf ball travels 500 in before it hits the Moon^?s surface. Just before hitting the surface, its speed is vA. Golfer B hits golf ball B at an angle of 15 degree above the horizontal on Earth, and the gold ball travels 100 m before it hits the Earth^?s surface. Just before hitting the surface, its speed is VB. What is the value of . The acceleration of gravity on the Moon is 1/6 that on Earth. (1) 1.14 (2) 1.65 (3) 0.96 (4) 0.73 (5) 0.21

Explanation / Answer

accelaration due to gravity on moon is g = 9.81/6 = 1.635 m/s^2

for golf ball A

time of flight is TA = u*sin(60)/g

Range R = u^2*sin(2*60)/g

500 = u^2*sin(120)/1.635 = 0.529*u^2

u = sqrt(500/0.529) = 30.7 m/s

TA = u*sin(60)/g = (30.7*sin(60))/1.635 = 16.3 s

for golf ball B

u = 18.08 m/s

TB = u*sin(15)/g = 18.08*sin(15)/1.635 = 2.86 s

then VA = sqrt(vx^2+vy^2)

vx = 30.7*cos(60) = 15.35 m/s

vy = uy-(g*TA) = (30.7*sin(60))-(1.635*16.3) = -0.0635 m/s

then VA = sqrt(15.35^2+0.0635^2) = 15.35 m/s

VB = sqrt(Vx^2+Vy^2)

vx = 18.08*cos(15) = 17.46 m/s

vy = (18.08*sin(15))-(1.635*2.86) = 0.0033m/s

VB = sqrt(17.46^2+0.0033^2) = 17.46 m/s

VB/VA = 17.46/15.35 = 1.44

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