Answer:
1. 2.12 seconds
2. 10 feet
Step-by-step explanation:
1. "Pekka tosses a ball out of a window that is 40 feet in the air. Its initial velocity is 15 feet per second. The path of the ball is represented by:
h = -16t² + 15t + 40
How long does it take for the ball to hit the ground (in seconds) rounded to the nearest hundredth?"
When the ball hits the ground, its height is 0:
0 = -16t² + 15t + 40
0 = 16t² − 15t − 40
Solve with quadratic formula:
t = [ -b ± √(b² − 4ac) ] / 2a
t = [ 15 ± √(225 + 2560) ] / 32
t ≈ 2.12 or -1.18
t must be positive, so t = 2.12 seconds.
2. "Tricia bounces a ball in front of her feet. The path of the ball from the time it hits the ground until it lands on the floor is represented by:
f(x) = -2(x − 3)² + 10
Assuming that Tricia's feet are located at the origin (0, 0), what is the maximum height of the ball (in feet)?"
The function is a parabola. The vertex of this parabola is at (3, 10). So the maximum height is 10 feet.
