Question

The height, in meters, after the launching of a projectile, and time, t, in seconds is defined: h = -3t^2 + 27. When was the projectile at a height of 24 meters?

a) t = 1 second
b) t = 3 seconds
c) t = 5 seconds
d) t = 7 seconds

Answer 1

The projectile was at a height of 24 meters at t = 1 second. This is found by setting the height equation h = -3t^2 + 27 equal to 24 and solving for t.

Step-by-step explanation:

The question asks at what time a projectile was at a height of 24 meters given the equation h = -3t^2 + 27. To find the time when the projectile is at 24 meters, we need to set the height equal to 24 meters and solve for t:

24 = -3t^2 + 27.

By rearranging the equation, we get:

-3t^2 + 27 = 24

-3t^2 = 24 - 27

-3t^2 = -3

t^2 = 1

t = ±1 second.

Since time cannot be negative in this context, the positive value is the correct answer. Therefore, the projectile was at a height of 24 meters at t = 1 second.