Or 2 tan sec 2 A baseball player hits a ball at an angle of

Or 2 tan sec 2. A baseball player hits a ball at an angle of 54° and at a height of 4.5 ft. If the ball\'s initial velocity after being hit is 152 ft./s and if no one catches the ball, when will it hit the ground? Remember that the acceleration due to gravity is 32 ft /s2 . O5.58 seconds O7.72 seconds O5.63 seconds 07.69 seconds 23. which set of parametric equations represents the function y = 3x2-29x +64 ? (1 point) x=t-4 y=3°-52+275 y=t2-9t +64 Cx=1+3 y=3\"-11+5

Solution

22)

acceleration a(t)=<0,-32>

initial velocity v(0)=<152cos54^o,152sin54^o>

initial position h(0)=<0,4.5>

v(t)=v(0)+a(t) dt

v(t)=<152cos54^o,152sin54^o>+<0,-32> dt

v(t)=<152cos54^o,152sin54^o>+<0,-32t>

v(t)=<152cos54^o,152sin54^o -32t>

h(t)=h(0)+v(t) dt

h(t)=<0,4.5>+<152cos54^o,152sin54^o -32t> dt

h(t)=<0,4.5>+<(152cos54^o)t,152sin54^o)t -16t²>

h(t)=<(152cos54^o)t,4.5+(152sin54^o)t -16t²>

when ball hits the ground ,4.5+(152sin54^o)t -16t²=0

=>t²-(9.5sin54^o)t =(4.5_/16)

=>t²-(9.5sin54^o)t+(4.75sin54^o)² =(4.5_/16)+(4.75sin54^o)²

=>(t-(4.75sin54^o))² =0.28125+(4.75sin54^o)²

=>t =4.75sin54^o+[0.28125+(4.75sin54^o)²]

=>t =7.7208

7.72 seconds

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23)

given y=3x²-29x+64

for x=t+4

y=3(t+4)²-29(t+4)+64

y=3(t²+8t+16)-29t-116+64

y=3t²+24t+48-29t-116+64

y=3t²-5t -4

second option x= t+4 , y=3t²-5t -4

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