Question

Porter jumps from a ledge that is 32 feet above a lake with an initial upward velocity of 16 feet per second. How long will it take until Porter enters the water?

A) 2 seconds
B) 3 seconds
C) 4 seconds
D) 5 seconds

Answer 1

Porter will not enter the water.

Step-by-step explanation:

To find how long it will take until Porter enters the water, we can use the equation h = ut + 0.5gt^2, where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time.

In this case, h = 32 ft, u = 16 ft/s, and g = -32 ft/s^2 (negative because the direction is downwards).

Substituting these values into the equation, we get: 32 = 16t - 16t^2.

Rearranging the equation to the standard quadratic form: -16t^2 + 16t - 32 = 0.

Simplifying the equation by dividing all terms by -16, we get: t^2 - t + 2 = 0.

Using the quadratic formula, we can solve for t: t = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = -1, and c = 2.

Calculating the values, we get t = (-(-1) ± √((-1)^2 - 4(1)(2))) / (2(1)).

Simplifying this further, we get t = (1 ± √(1 - 8)) / 2.

The discriminant, 1 - 8, is negative, indicating that there are no real solutions for t. Therefore, Porter does not enter the water.