A diver jumps into a pool (on earth) from a diving board 21 meters above the water.

Question

A diver jumps into a pool (on earth) from a diving board 21 meters above the water. If it takes 3.28 seconds for her to reach the water, what was the vertical component of her velocity, in units of m/s?

Answer should be 9.6696 m/s

I cannot find any equation online which would be applicable to solving this.

Answer 1

Hi Sam,

The motion of this diver is influenced solely by gravity, and so the kinematic equations describing this problem are:

a(t) = -g

v(t) = -gt + v₀

h(t) = -(1/2)gt² + v₀t + h₀

where a is acceleration, v is vertical component of velocity, and h is height above the ground (pool)

Using equation 3, we see that when the diver hits the ground (at time t = 3.28 s according to the problem):

h(3.28) = -(1/2)g(3.28)² + v₀(3.28) + 21 = 0

(because at 3.28 s, the diver hits the pool (height zero))

Solve this equation for v₀ and you will have your answer.

If you would like more insight on these kinematic equations and how to apply them to all kinds of problems, please reach out to me.