Final answer:
The height of the ball will be 37 feet when the ball is travelling towards the ground after approximately 2 seconds.
Step-by-step explanation:
To find the time it will take for the ball to be at a height of 37 feet when it is travelling towards the ground, we need to set the height function equal to 37 and solve for t:
-16t² + 48t + 5 = 37
-16t² + 48t - 32 = 0
We can solve this quadratic equation using the quadratic formula: t = (-b ± √(b² - 4ac)) / (2a). In this case, a = -16, b = 48, and c = -32.
Plugging in these values, we get: t = (-48 ± √(48² - 4(-16)(-32))) / (2(-16)).
Simplifying further, we have: t = (-48 ± √(2304 - 2048)) / (-32).
This simplifies to: t = (-48 ± √256) / (-32).
Since we're interested in when the ball is travelling towards the ground, we take the positive value of t: t = (-48 + 16) / (-32). Solving, we find that t is approximately 2 seconds.