(Physics) In Olympic diving the highest dive is from the 10 meter platform. For a diver who steps off of the platform calculate… how long in seconds does it take to hit the water?

Answer 1

A: The only information provided is the 10 m distance between the diving platform and the pool’s surface. This necessitates the use of a kinematic equation that relates distance and the acceleration due to gravity ( g ) experienced by a diver in free-fall: 

x = vot +/- ½ at2, where x = displacement experienced by an accelerating object relative to its initial position, vo = initial velocity, a = gravitational constant of acceleration ( g ), and t = time it takes for the diver to reach the pool’s surface.

We must first choose a sign designation ( + or - ) for the vertical ( y ) direction of travel. If the upward direction is designated as ( +y ), the downward designation is ( -y ). After choosing a sign designation, we must determine how gravity will influence the velocity ( v ) of the diver. If we designate the upward direction as ( +y ), a diver that jumps upward will have a non-zero initial velocity that is positive ( +v ); however, the force of gravity is working in the ( -y ) direction. In this circumstance, the diver’s initial upward motion will decrease as time transpires. As a consequence, acceleration due to gravity ( deceleration ) is designated as ( - g ) in this circumstance. Thus, y = voyt - ½ gt2 models a POSITIVE initial velocity that will DECREASE in value over time. Conversely, if the diver flips horizontally off the diving board, the initial velocity ( voy ) is zero. In this circumstance, the diver would fall freely in the ( -y ) direction. This motion is modeled as -y = 0 - ½ gt2.

It is given that a diver steps off of a 10 m platform. If the downward direction is designated as being ( +y ), acceleration due to gravity will add to the motion of the diver. Therefore, in this circumstance, ( y ) and the gravitational constant of acceleration ( g ) will be assigned a positive value. In mathematical form, this leads to +y = 0 + ½ gt2. Further simplification leads to +2y = gt2. Dividing both sides of the equation by ( g ), we have ( +2y/g ) = t2. Finally, √( +2y/g ) = t.

The √[ ( +2 )( +10 m ) / ( +9.8 m/s2 ) ] = 2 s.