A ball is thrown eastward into the air from the origin (in the direction of the

Question

A ball is thrown eastward into the air from the origin (in the direction of the positive x-axis). The initial velocity is 50 i + 64 k, with speed measured in feet per second. The spin of the ball results in a southward acceleration of 6 ft/s^2, so the acceleration vector is a = -6 j - 32 k. Where does the ball land? (Round your answers to one decimal place.) ft/s ft from the origin at an angle of degree from the eastern direction toward the south. With what speed does the ball hit the ground? (Round your answer to one decimal place.)

Explanation / Answer

a=-6j -32k

v(t)= a dt

v=ci +(-6t+d)j +(-32t+e)k

initial velocity v(0)=50 i +64 k

ci +(-6*0 +d)j +(-32*0 +e)k=50 i +64 k

==>c=50 , d=0 , e= 64

v=50i -6tj +(-32t+64)k

position s(t)= vdt

s(t)=50i -6tj +(-32t+64)k dt

s=(50t)i -(3t2)j +(-16t2+64t)k

when ball lands component of k is zero

-16t2+64t=0

==>t=4

ball lands after 4 sec

s(4)=(50*4)i -(3*42)j +(-16*42+64*4)k

s(4)=200i-48j

|s|=(2002+(-48)2) =205.7 ft from origin

angle =tan-1(48/200)=13.5ofrom east towards south

v(4) =v=50i -24j -64k

speed =|v|=(502+(-24)2+(-64)2)=84.7ft/sec

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.