After leaving a platform, the velocity with which a diver enters the water is directly proportional to the
square root of the height of the platform. When a diver jumps off a 10-meter platform, they will strike
the water at 46 feet per second. In Acapulco, Mexico cliff divers plunge 135 feet into the water below.
I assume you want the velocity from that height.
v = k√h
so, v/√h = k, a constant.
so, you want v such that
v/√135 = 46/√(10*3.28)
To solve this problem, we can use the concept of direct proportionality and the given information to find the velocity at which the diver will enter the water when jumping from a 135-feet platform.
Let's first write down the proportionality relationship:
Velocity ∝ √(height of the platform)
Now, let's use the given information:
When the height of the platform is 10 meters, the velocity is 46 feet per second.
To make the calculations easier, let's convert the units:
10 meters is approximately 32.8 feet.
So, we have the following values:
Height of the 10-meter platform = 32.8 feet
Velocity at the 10-meter platform = 46 feet per second
Using this information, we can set up the proportionality equation as follows:
Velocity/√(Height of the 10-meter platform) = Velocity at the 135 feet platform/√(Height of the 135 feet platform)
Now, let's substitute the values we have:
46/√(32.8) = Velocity at the 135 feet platform/√(135)
To find the velocity at the 135 feet platform, we can cross-multiply and solve for it:
Velocity at the 135 feet platform = (46/√(32.8)) * √(135)
Using a calculator, we can evaluate this expression to find the velocity at the 135-feet platform, which is approximately 68.58 feet per second.
Therefore, when a diver jumps off a 135-feet platform, they will strike the water at approximately 68.58 feet per second.