Question

The height after t seconds of an object projected upward with an initial velocity of 48 feet per second from a 210-foot tower can be modeled by h=−16t^2 + 48t +210. The height of a neighboring 50-foot tall building is modeled by the equation h=50. The time (t) when the object will be at the same height as the building is found to be t = –2 and t =5. Which statement BEST describes the validity of these solutions?

A. Neither solution is valid since time values cannot be squared.

B. The solution t = – 2 is the only solution since 5 seconds is an unreasonable amount of time for the object to reach a height of 50 feet.

C. The solution t = 5 is the only valid solution to this system since time cannot be negative.

D. Both are valid solutions to this system since both values make the equation h=−16t^2 + 48t + 210 true.

Answer 1

C. The solution t = 5 is the only valid solution to this system since time cannot be negative.

Explanation:

Given

`h(t) = -16t^2 + 48t + 210`

`h(t) = 50`

Required

Determine which of the options is true

After solving

`h(t) = -16t^2 + 48t + 210`

for

`h(t) = 50`

We have that

`t = -2` and
`t = 5`

Because time can't be negative, we have to eliminate
`t = -2`

So, we're left with

`t = 5`

Because of this singular reason, we can conclude that option c answers the question