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) 27 seconds later
B) 125 seconds later
C) 25 seconds later
D) 17 seconds later
E) 33 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) 27 seconds later 
B) 125 seconds later 
C) 25 seconds later 
D) 17 seconds later 
E) 33 seconds later

Quizplus · Accepted Answer

The bullet will land when its height above the ground is 0. Let's set the equation 11ec08ab_f52d_ec62_ae58_17e23cd48689_TBX8808_11 = 0 and solve for t:

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

Simplifying:

16t^2 - 383t + 425 = 0

Using the quadratic formula:

t = (383 ± sqrt(383^2 - 4(16)(425))) / (2(16))

t = (383 ± sqrt(136089)) / 32

t = (383 ± 369) / 32

t = 25/8 or 17/4

Since the negative solution doesn't make sense in this context, we take the positive solution: t = 25/8 = 3.125

So the bullet will land 3.125 seconds after it was fired, which is approximately 25 seconds later. Therefore, the answer is C.

A Gun Fires a Bullet Almost Straight Up from the Edge