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?
The time to fall H = 150 feet is
t = sqrt(2H/g)= 3.05 seconds
The horizontal motion in that time will be
10 ft/s*3.05 = 30.5 feet
He will hit the rocks before he hits the water.
To determine whether the diver will land in the water or not, we need to compare the horizontal distance he can cover with his forward motion (10 ft/s) to the distance between the top edge of the cliff and the water's edge (38 ft).
Let's calculate the time it takes for the diver to fall to the water using the vertical distance he needs to cover (150 ft). We can use the formula:
time = vertical distance / vertical velocity
Since the vertical velocity is influenced by the acceleration due to gravity, we can assume it to be approximately 32 ft/s^2 (ignoring air resistance).
time = 150 ft / 32 ft/s^2
time ≈ 4.69 s
Now that we know it takes around 4.69 seconds for the diver to fall, we can calculate the horizontal distance he covers during this time. Horizontal distance can be calculated using:
horizontal distance = forward motion velocity * time
In this case, the forward motion velocity is given as 10 ft/s, which can be multiplied by the time determined earlier.
horizontal distance = 10 ft/s * 4.69 s
horizontal distance ≈ 46.9 ft
Comparing the horizontal distance covered (46.9 ft) to the distance between the top of the cliff and the water's edge (38 ft), we can conclude that the diver will indeed land in the water.
Therefore, the diver will land safely in the water when jumping off the 150 ft cliff in Acapulco, given their forward motion of 10 ft/s and the 38 ft extension of the base of the cliff beyond the top edge.