Need help on 3d, 3e, 3g,3i Introduction Part II When you throw an object up, its

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Need help on 3d, 3e, 3g,3i
Introduction Part II When you throw an object up, its speed keeps decreasing because of gravity. The speed that you throw the object up at is called its init velocity. If you throw an object upwards with initial velocity vo feet per second, the height above its starting point aftert seconds is given by h()--162+ vot. Examples If you throw a rock up from the ground with an initial velocity of 32t ft/sec, its height above the ground after t seconds is given by h(t)--16t2+32. 3. A ball is thrown up from a cliff 120 feet above the ground. It is thrown up with the an initial velocity of 64 feet per second. On the way down the ball does not hit the cliff but continues on until it hits the ground. The height of the ball (in feet) above the cliff after 1 seconds is given by h(t)=-162 + 64. a. Use the function h(t) to find the height of the ball above the cliff after zero seconds. Does your answer make sense? What is the height of the ball above the ground at this time? b. Find the height of the ball above the cliff after one second. What is the height of the ball above the ground at this time? c. Find a function, g(t), which expresses the height of the ball above the ground after t seconds. Check your formula by substituting t 20,1, and comparing with parts a and b above. sec ve.nsec, 64 Use your function g(t) to answer the following questions. Your function should be g(t)--162 +64t+120. Check that this is what you have. d. When does the ball hit the ground? e. What is the highest that the ball gets? When does this occur? , f. Graph the function y=g(t),fromtime 0 until the ball hits the ground. Label the coordinates of three key points - the vertex of the parabola; the point that shows the height of the ball at time 0; and the point that corresponds to when the ball hits the ground.

Explanation / Answer

h(t)=-16t 2+64t

3.d. Hit the ground means h(t)=0

-16t 2+64t=0

-16t(t-4)=0

t=0,4

e.height is maximum at the vertex which is t=-64/(2(-16))=2

h(2)=-16(4)+64(2)=64feet

g.height above the cliff=168-120=48feet

-16 t 2+64t=48

16t 2-64t+48=0

t 2-4t+3=0

t=1sec , 3 sec

i.Height above cliff=200-120=80feet

-16t 2+64t=80

16t 2 -64t+80=0

t 2 -4t+5=0

(t-5)(t+1)=0

t=5secs

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