SOLUTION: A bullet is fired from a gun and made a projectile motion. The trace of the path of the bullet is mathematically expressed as d = 60t — 4t2, where d is the distance in meters of
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-> SOLUTION: A bullet is fired from a gun and made a projectile motion. The trace of the path of the bullet is mathematically expressed as d = 60t — 4t2, where d is the distance in meters of
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Question 1165760: A bullet is fired from a gun and made a projectile motion. The trace of the path of the bullet is mathematically expressed as d = 60t — 4t2, where d is the distance in meters of the bullet from the ground in t seconds.
a. What is the distance of the bullet from the ground after 2 seconds (s)?
b. At what time will the bullet reach a height of 200 m?
c. What maximum distance from the ground does the bullet reach?
d. After how many seconds does the bullet reach its highest point?
e. At what time will the bullet hit the ground? Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! d=60t-4t^2
so d(2)=120-16=104 m.
200=-4t^2+60t
so 4t^2-60t=200=0
and
t^2-15t+50=0, dividing by 4
(t-10)(t-5)=0
so at t = 5 and 10 seconds
maximum distance up is at the vertex or t=-b/2a That is 60/8 or 7.5 seconds.
d(7.5)=450-225=225 m
It hits the ground after 15 seconds, twice the time it takes to reach the highest point.
one could also do 4t^2-60t=0
t^2-15t=0
t(t-15)=0
t=0 (start) and t=15 seconds.
