50 i + 80 k , with speed measured in feet per second. The spin of the ball resul

Question

50 i + 80 k, with speed measured in feet per second. The spin of the ball results in a southward acceleration of 10 ft/s2, so the acceleration vector is a = ?10 j ? 32 k. Where does the ball land?

A ball is thrown eastward into the air from the origin (in the direction of the positive x-axis). The initial velocity is 50i 80 k, with speed measured in feet per second. The spin of the ball results in a southward acceleration of 10 ft/s2, so the acceleration vector is a =-10 j-32 k, where does the ball land? (Round your answers to one decimal place.) X ft from the origin at an angle of Xf ° from the eastern direction toward the south. Enter a number With what speed does the ball hit the ground? (Round your answer to one decimal place.)

Explanation / Answer

givedn acceleration a(t)=0i-10j-32k

velocity v(t)=0i-10j-32k dt

v(t)=(0i-10tj-32tk )+c

given initial velocity v(0)=50i +0j +80k

(0i-10*0j-32*k )+c=50i +0j +80k

=>c=50i +0j +80k

v(t)=(0i-10tj-32tk )+(50i +0j +80k)

v(t)=50i-10tj+(-32t+80)k

position s(t)=50ti-5t2j+(-16t2+80t)k +c

at origin positiion of ball s(0)=0

c=0

s(t)=50ti-5t2j+(-16t2+80t)k

when ball hits ground -16t2+80t =0

-16t(t-5)=0

t-5=0

t=5sec

s(5)=250i-125j+0k

angle =tan-1(-125/250)

angle = -26.5650

ball lands 26.5650 from the eastern direction towards south

v(5)=50i-10tj+(-80)k

speed with which ball hits the ground =[502+102+(-80)2]=94.9 ft/s

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