Question

The equation h(t) = -16t²+19t+3 models the path of a projectile where h is the height of the object in feet and t is the time in seconds.

#1 What method is the most appropriate for solving the equation when 0=-16t²+19t+3?

#2 What will the value of t represent when the equation 0 = -16t² +19t + 3 is solved?

#3 Solve the equation. Which solution(s) make sense in the context of the model? Round to the nearest hundredth.

Pls, Help I need this before tomorrow.

Answer 1

#1 The most appropriate method for solving the equation 0 = -16t² +19t + 3 is factoring.

#2 The value of t will represent the time in seconds when the height of the projectile is 0 feet. This means that t represents the time at which the projectile hits the ground.

#3 To solve the equation, we need to get t on one side of the equation and all the other terms on the other side. To do this, we can add 16t² to both sides of the equation to get:

16t² = -19t - 3

Next, we can factor the right side of the equation as:

16t² = -t(19) - 3

And, we can divide both sides of the equation by -1 to get:

-16t² = t(19) + 3

Finally, we can divide both sides of the equation by 19 to get:

t = (-3)/19 or t = (19)/16

The solution t = (-3)/19 doesn't make sense in the context of the model, as time cannot be negative. The solution t = (19)/16 represents the time in seconds when the height of the projectile is 0 feet. Rounding to the nearest hundredth, we have:

t ≈ 1.19

So, the time at which the height of the projectile is 0 feet is approximately 1.19 seconds.