Final answer:
The cat is approximately 9.6 feet from the base of the boulder when it lands on the ground. The maximum height of the cat during its jump is 7 feet.
Step-by-step explanation:
To find how far the cat is from the base of the boulder when it lands on the ground, we need to find the value of d when h is 0. Using the equation h = -0.5d² + 2d + 5, we can set h to 0 and solve for d.
0 = -0.5d² + 2d + 5
0 = -d² + 4d + 10
Using the quadratic formula or factoring, we can find that the roots are approximately -0.41 and 9.59.
Since the cat cannot be -0.41 feet from the base of the boulder, we can round the value of d to the nearest tenth and say that the cat is approximately 9.6 feet from the base of the boulder when it lands on the ground.
To find the maximum height of the cat during its jump, we need to find the vertex of the parabolic equation h = -0.5d² + 2d + 5.
The x-coordinate of the vertex can be found by using the formula x = -b / (2a), where a is the coefficient of d² and b is the coefficient of d. In this equation, a = -0.5 and b = 2.
x = -2 / (2 * -0.5) = 2
Substituting the x-coordinate of the vertex back into the equation, we can find the y-coordinate (which represents the height) of the vertex:
h = -0.5(2)² + 2(2) + 5
h = -0.5(4) + 4 + 5
h = -2 + 4 + 5 = 7
Therefore, the maximum height of the cat during its jump is 7 feet.