4. a diver of mass m drops from a board 10.0 m above the water's surface. neglect air
resistance.
a. find the diver's speed 5.00 m above the water's surface.
b. find the diver's speed at the water's surface

answer and dont ignore

This question involves the concept of the equations of motion.

a. The diver's speed at 5 m height above the water's surface will be "98.1 m/s".

b. The diver's speed at the water's surface will be "196.2 m/s".

We can use the third equation of motion to find out the speed of the diver at different heights:

where,

g = acceleration due to gravity = 9.81 m/s²

h = height lost

v_f = final speed = ?

v_i = initial speed = 0 m/s

Therefore,

a.

Here,

h = 5 m

Therefore,

b.

Here,

h = 10 m

Therefore,

Learn more about equations of motion here:

link

The attached picture shows the equations of motion.

Explanation:

a. KE + PE = PE at top

½ mv² + mgh₁ = mgh₂

½ v² + gh₁ = gh₂

½ v² = g (h₂ − h₁)

v = √(2g (h₂ − h₁))

v = √(2 × 9.8 m/s² × (10.0 m − 5.00 m))

v = 9.90 m/s

b. v = √(2g (h₂ − h₁))

v = √(2 × 9.8 m/s² × (10.0 m − 0 m))

v = 14.0 m/s

the area between the graph and the t axis