Question

URGENT ! 100 POINTS

It's the age of Vikings! You are an archer on a boat approaching the London bridge in England with troops ready to ambush and secure London, England. Your leader yells
to ready your aim to fire as the boat rushes at full speed towards your enemies ahead!

Steadily, you line up the shot and the arrow is launched from your bow into the air with an upward velocity of 60ft/sec. The equation that gives the height (h) of the arrow at any time (t), in seconds, is modeled by:
h(t) = − 16t²+60t + 9.5

How long will it take the arrow to reach the enemy on the bridge and nail him with a
perfect headshot?

(The enemies head is about 45 feet from ground level as he is located on top of the London bridge)

Answer 1

To find out how long it will take for the arrow to hit the enemy on the bridge, we need to find the time when the height of the arrow is 45 feet (the height of the enemy's head above the ground).

So, we can set h(t) equal to 45 and solve for t:

h(t) = − 16t²+60t + 9.5

45 = −16t² + 60t + 9.5

Rearranging the equation, we get:

16t² - 60t - 35.5 = 0

To solve for t, we can use the quadratic formula:

t = (-b ± sqrt(b² - 4ac)) / 2a

where a = 16, b = -60, and c = -35.5

Plugging in the values, we get:

t = (-(-60) ± sqrt((-60)² - 4(16)(-35.5))) / 2(16)

Simplifying the expression inside the square root, we get:

t = (60 ± sqrt(3600 + 2272)) / 32

t = (60 ± sqrt(5872)) / 32

t ≈ 0.81 or t ≈ 3.69

Since we're looking for the time when the arrow hits the enemy, we need to choose the positive solution: t ≈ 3.69 seconds.

Therefore, it will take approximately 3.69 seconds for the arrow to hit the enemy on the bridge with a perfect headshot.