A diver in Acapulco jumps off a 150 ft cliff. His forward motion is 10 feet per second. The base of the cliff at the waters edge extends 38 feet beyound the top edge of the cliff. Will the diver land in the water?
To determine whether the diver will land in the water, we need to calculate the horizontal distance the diver will travel before reaching the water.
First, let's convert the measurements to a common unit. Since the velocity given is in feet per second, we'll work with feet.
The height of the cliff is given as 150 ft, and the base extends 38 ft beyond the top edge. So the total distance from the top of the cliff to the landing point would be 150 ft + 38 ft = 188 ft.
Now, let's calculate the time it takes for the diver to fall from the cliff to the water. We know the vertical distance (height of the cliff) and the initial vertical velocity (0 ft/s because the diver jumps straight down). Using the equation of motion, s = ut + (1/2)at^2, where s is the distance, u is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2), we can solve for time.
Plugging in the values:
s = 150 ft
u = 0 ft/s
a = -32.2 ft/s^2
150 = 0t + (1/2)(-32.2)t^2
300 = -32.2t^2
-32.2t^2 = 300
t^2 = 300 / -32.2
t^2 ≈ -9.32
Since the resulting time squared is negative, it means that the quadratic equation has no real solutions. In other words, there is no real answer to this calculation. This indicates that the diver will never hit the water, and he will fall 188 ft horizontally before reaching the water.
Therefore, based on the given information, the diver will not land in the water.