Question

1. A projectile is launched upward at an angle so that its distance (in feet) above the ground after ? seconds is given by the function
     ?(?) = −20?2 + 105?   Round each answer to the nearest hundredth. a. When (i.e., how many seconds after launch) will the projectile reach its maximum height?
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b. How many seconds after launch will it take for the projectile to return to earth?
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c. What is the maximum height achieved by the projectile during flight?
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Answer 1

Given function is : f(x) = -20x²+105x

a) Here,

i.e.,

Now, gives -40x+105 = 0

i.e., x = 105/40

i.e., x = 2.625

i.e., x 2.63

Therefore, 2.63 seconds after launch the projectile will reach its maximum height.

b) Now, f(x) = 0 gives -20x²+105x = 0

i.e., -(20x²-105x) = 0

i.e., 20x²-105x = 0

i.e., 5x(4x-21) = 0

i.e., x(4x-21) = 0

i.e., x = 0 and x = 21/4

i.e., x = 0 and x 5.25

Here, x = 0 indicates the initial time when the projectile will be launched.

Therefore, 5.25 seconds after launch, the projectile will return to the Earth.

c) Putting x = 2.625 in the function we get,

f(2.625) = -20(2.625)²+105(2.625)

i.e., f(2.625) = 137.8125

i.e., f(2.625) 137.81

Therefore, the maximum height achieved by the projectile during flight is 137.81 feet.