1)
The polynomial modelling this scenario is expressed as
P(t) = - 16t^2 + 300t
where
P(t) represents the height at time t
a) To find the height of the projectile when t = 1 second, we would substitute
t = 1 into the equation. Thus,
P(1) = - 16(1)^2 + 300(1)
P(1) = - 16 + 300 = 284
Height of projectile when t = 1 second is 284 feet
b) To find the height of the projectile when t = 5 second, we would substitute
t = 5 into the equation. Thus,
P(1) = - 16(5)^2 + 300(5)
P(1) = - 400 + 1500
Height of projectile when t = 5 second is 1100 feet
c) At the time when the object hits the ground, the height would be zero. This means that p(t) = 0
Thus, the equation would be
0 = - 16t^2 + 300t
Factoring out 4t from the right, we have
0 = - 4t(4t - 75)
- 4t = 0 or 4t - 75 = 0
t = 0/-4 or 4t = 75
t = 0 or t = 75/4
t = 0 or t = 18.75
It will take 18.75 seconds until the object hits the ground
