Question

A projectile is fired upward from the ground with an initial velocity of 300 feet per second. Neglecting air resistance, the height of the projectile at any time I can be described by the polynomial function P(t) = -16t^2 +300t. Find the height of the projectile at each given time.t = 1 sect = 2 sect = 10 sect = 14 sec

Answer 1

Given the polynomial function:

`P(t)=-16t^2+300t`

Where, 300 feet per second is the initial velocity.

To find the height of the projectile at each given time, substitute the given time for t and evaluate.

We have:

• t = 1 sec

`\begin{gathered} P(1)=-16(1)^2+300(1) \\ \\ P(1)\text{ = -16}+300 \\ \\ P(1)=\text{ 284 f}eet \end{gathered}`

• t = 2 sec

`\begin{gathered} P(2)=-16(2)^2+300(2) \\ \\ P(2)=-16(4)+600 \\ \\ P(2)=-64+600 \\ \\ P(2)=236\text{ fe}et \end{gathered}`

• t = 10 sec

`\begin{gathered} P(10)=-16(10)^2+300(10) \\ \\ P(10)=-16(100)+3000 \\ \\ P(10)=-1600+3000 \\ \\ P(10)=1400\text{ fe}et \end{gathered}`

• t = 14 sec

`\begin{gathered} P(14)=-16(14)^2+300(14) \\ \\ P(14)=-16(196)+4200 \\ \\ P(14)=-3136+4200 \\ \\ P(14)=1064\text{ fe}et \end{gathered}`