The function h=t^2 +95 models the path of a ball is in the air. assuming the boy lives at sea level where h=0 ft, which is a likely place the boy could have been standing when he threw this ball?
a. his backyard
b. an underground cave
c. a ladder
d. a bridge
Lacking data.
The equation h = t^2 + 95 represents the height (h) of the ball at any given time (t). Since the boy lives at sea level where h = 0 ft, we can find the likely place the boy could have been standing when he threw the ball by determining the height at time t = 0.
Substituting t = 0 into the equation, we get:
h = (0)^2 + 95 = 0 + 95 = 95 ft
Therefore, a likely place the boy could have been standing when he threw the ball is a bridge (option d) where the height is typically above sea level.
To determine a likely place the boy could have been standing when he threw the ball, we need to find the height at which the ball was released (when h = 0 ft).
Given the function h = t^2 + 95, where t is the time in seconds and h is the height in feet, we can set h = 0 and solve for t.
0 = t^2 + 95
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 0, and c = 95. Plugging these values into the quadratic formula, we get:
t = (-0 ± √(0^2 - 4 * 1 * 95)) / (2 * 1)
t = ± √(-380) / 2
Since the value inside the square root is negative, this means there are no real solutions for t. This implies that the ball never reaches a height of 0 ft during its flight, and therefore, the boy must have thrown the ball from a location above sea level.
Therefore, the likely place the boy could have been standing when he threw the ball is d. a bridge, since bridges are typically elevated above sea level.