1. While marching in a band, a drum major tosses a baton into the air and catche
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Question
1. While marching in a band, a drum major tosses a baton into the air and catches it. The height (in feet) of the baton after t seconds can be modeled by h=-16t^2 +32t+6. Find the maximum height of the baton. Determine how long is the air if the height at which the drum major catches it is 4 feet.
2. The height h(t) of a baseball t seconds after it is hit is gven by the formula h(t)=-16t^2+48t+2. Find the maximum height of the ball and when the baseball hits the ground.
3. Flying fish use their pectoral fins like airplane wings to glide throught the air. The path of the fish can be modeled by the quadratic function y= -5/1089(x-33)^2 +5. Whe does the fish reach its maximum height, what is the fish's maximum height , and how far can it fly before it reenters the water?
4. The arch of the Gateshead Millennium Bridge forms a parabola with the equation y= -0.016(x-52.2)^2+45 where x is the horizontal distance in meters from the arch's left end and y is the distance in meters from the base of the arch. What is the width of the arch?
5. The flight of a golf shot can be modeled byt he function y= -0.001x(x-260) where x is the horizontal distance in yards from the impact point and y is the height in yards. How many yards away fromt he impact point does the ball land and what is the maximum height of the golf shot?
6. The function h(x) + -0.0035x(x-143.9) models the path of the water sot by a water cannon where x is the horizontal distance (in feet) and h(x) is the corresponding height (in feet). How far does the water shoot? What is the maximum height of the water?
Explanation / Answer
1. While marching in a band, a drum major tosses a baton into the air and catches it. The height (in feet) of the baton after t seconds can be modeled by h=-16t^2 +32t+6. Find the maximum height of the baton. Determine how long is the air if the height at which the drum major catches it is 4 feet.
-- h= -16t^2 +32t+6
maximu height ocurs at vertex : t = -b/2a = -(32/2*-16) = 1
h (1) = -16*1 +32 +6 = 22 ft
h(t) = 4; 4 = -16t^2 +32t+6
-8t^2 + 16t + 1 =0
t = -0.06 , 2.06 . Neglect -ve time
So, t = 2.06 sec
2. The height h(t) of a baseball t seconds after it is hit is gven by the formula h(t)=-16t^2+48t+2. Find the maximum height of the ball and when the baseball hits the ground.
h(t)=-16t^2+48t+2
Maximu height ocurs at vertex : t = -b/2a = - (48/2*-16) = 48/32 =12/8 = 3/2 = 1.5 sec
h(1.5) = - 16(1.5)^2 + 48*1.5 +2 = 38 ft
Whn ball hits ground : h(t) =0
0= -16t^2+48t+2
solve for t : t= -0.04, 3.04
Neglect -ve t
So, t = 3.04 sec before ball hits ground
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