SOLUTION: A bullet is fired in the air vertically from ground level with an initial velocity of 354 m/s. Find the bullet's maximum velocity and maximum height. (Assume g = 9.8 m/s2. Round

Question 1021123: A bullet is fired in the air vertically from ground level with an initial velocity of 354 m/s. Find the bullet's maximum velocity and maximum height.
(Assume g = 9.8 m/s2.
Round your answers to the nearest whole number.)
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
From Newton's 2nd law of motion, assuming that gravity is the only force acting on the bullet, we get
F = ma = -mg, where a is acceleration, and g = 9.8 .
Now , and so

==> for some constant k. (Note that dx/dt is the velocity.)
At t=0, dx/dt corresponds to the initial velocity, and so
354 = k
==>
==> for some constant c.
Since the bullet was fired from level ground, c = 0
==>
Maximum height happens when dx/dt = 0, or -9.8t+354 = 0, or t = 36.12244898.
=> max height is meters.
Maximum velocity of 354 m/s happens at the roots of x(t), namely t = 0, t = 36.12244898
(at the moments of initial release and return to the ground).
Minimum velocity happens at the maximum height, where velocity is 0 m/s.

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