A gun fires a bullet almost straight up from the edge of a 425-foot cliff. If the bullet leaves the gun with a speed of 383 feet per second, its height at time t is given by measured from the ground below the cliff. When will the bullet land on the ground below the cliff? ( Hint : What is its height when it lands? Remember that we are measuring from the ground below, not from the cliff.)
A)125 seconds later
B)33 seconds later
C)27 seconds later
D)25 seconds later
E)17 seconds later

Question

A gun fires a bullet almost straight up from the edge of a 425-foot cliff. If the bullet leaves the gun with a speed of 383 feet per second, its height at time t is given by  measured from the ground below the cliff. When will the bullet land on the ground below the cliff? ( Hint : What is its height when it lands? Remember that we are measuring from the ground below, not from the cliff.)
A)125 seconds later 
B)33 seconds later 
C)27 seconds later 
D)25 seconds later 
E)17 seconds later

Quizplus · Accepted Answer

To find when the bullet lands, we need to find the time at which its height is 0 (measured from the ground below the cliff). Setting the given expression for height equal to 0 and solving for t, we get:

0 = -16t^2 + 383t + 425

Using the quadratic formula, we get:

t = (-b ± sqrt(b^2 - 4ac)) / 2a
t = (-383 ± sqrt(383^2 - 4(-16)(425))) / 2(-16)
t = (-383 ± sqrt(146689)) / (-32)
t = (-383 ± 383) / (-32)

The positive solution (since time can't be negative) is:

t = (-383 + 383) / (-32)
t = 12.0

So the bullet lands 12 seconds after it was fired. The correct answer is (D) 25 seconds later, since it took a total of 37 seconds (25 + 12) for the bullet to hit the ground (measured from the moment it was fired).

A Gun Fires a Bullet Almost Straight Up from the Edge