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.

Respuesta :

Answer:

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

Step-by-step explanation:

Given

[tex]h(t) = -16t^2 + 48t + 210[/tex]

[tex]h(t) = 50[/tex]

Required

Determine which of the options is true

After solving

[tex]h(t) = -16t^2 + 48t + 210[/tex]

for

[tex]h(t) = 50[/tex]

We have that

[tex]t = -2[/tex] and [tex]t = 5[/tex]

Because time can't be negative, we have to eliminate [tex]t = -2[/tex]

So, we're left with

[tex]t = 5[/tex]

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