To signal the start of a 10 km is an official fired a blank bullet vertically up into the air. the initial velocity of the bullet is 120 feet per second and the distance covered above the ground after t seconds is represented by the equation s = 120 -16t².
a. How many seconds would it take for the the bullet to reach 216 feet?
b. Would the bullet reach a stationary kite 900 feet above? Why or why not?
Answers
Answer:
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Step-by-step explanation:
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Given : initial velocity of the bullet is 120 feet per second
the distance covered above the ground after t seconds is represented by the equation s = 120t -16t². ( correction)
To Find : a. How many seconds would it take for the the bullet to reach 216 feet?
b. Would the bullet reach a stationary kite 900 feet above? Why or why not?
Solution:
s = 120t - 16t²
s = 216
=> 216 = 120t - 16t²
=> 27 = 15t - 2t²
=> 2t² -15t + 27 = 0
=> 2t² - 6t - 9t + 27 = 0
=> 2t(t - 3) - 9(t - 3) =0
=> (2t -9 ) ( t - 3) = 0
=> t = 9/2 , t = 3
Hence Bullet will take 3 secs to reach a height of 216 ft
However after 9/2 sec again bullet will be at height of 216 ft
s = 120t -16t².
ds/dt = 120 - 32t
ds/dt = 0 => t = 120/32 = 15/4 secs
d²s/dt² = - 32 <0
Hence maximum s is at t = 15/4 sec
So Max height
= 120 ( 15/4) - 16(15/4)²
= 450 - 225
= 225
Hence Max height achieved is 225 ft only
so bullet can not reach a stationary kite 900 feet above
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