Question

the catapult at warwick castle in england is one of the largest working catapults in the world. during reenactments they demonstrate its capabilities by hurling an 80-pound fireball along the banks of the river avon. suppose the height of the fireball, in meters, is given by $h(t) = -4.9t^2 + 36t + 25$, where $t$ is the time in seconds since it left the cataput. a) how high in the air is the fireball after 5 seconds? $h(5) = \square$ meters b) how high was the fireball when it initially left the catapult? $h(0) = \square$ meters

Explanation:

Step1: Substitute t=5 into h(t)

$h(5) = -4.9(5)^2 + 36(5) + 25$

Step2: Calculate each term

$h(5) = -4.9(25) + 180 + 25 = -122.5 + 180 + 25$

Step3: Sum the values

$h(5) = 82.5$

Step4: Substitute t=0 into h(t)

$h(0) = -4.9(0)^2 + 36(0) + 25$

Step5: Simplify the expression

$h(0) = 0 + 0 + 25 = 25$

Answer:

a) $h(5) = 82.5$ meters
b) $h(0) = 25$ meters