please answer?

Question

A diver springs upward with an initial speed of 8 m/s from a diving board that is 3 m above the water.

a.) What is the maximum height the diver reaches above the water?
m

b.) Find the total time the diver is airborne.
s

c.) Will the diver spend more time travelling upwards or downwards? Explain.

Answer 1

for constant acceleration:
v(t) = speed after t seconds = v0 + a*t
h(t) = height after t seconds = h0 + v0*t + 0.5*a*t^2

where a is the acceleration.
For gravity, we use g instead of a but the equations remain the same and g = -9.8 m/s^2 (we set - to mean downward)

Here, v0 = +8 m/s (we'll set + means upwards) and
h0 = + 3 m

How long until the diver's height is 0?
We want to find t when h(t)=0

0 = +3 + 8*t + 0.5*(-9.8)*t^2

This is a quadratic (we rearrange the order):

-4.9 t^2 + 8t + 3 = 0

t ={ -8 +/- SQRT[64 - 4*(-4.9)*3]} / (2*-4.9)

t = { -8 +/- SQRT[64 + 58.8]}/-9.8
t = { -8 +/- SQRT[122.8]}/-9.8
t = { -8 +/- 11.08}/-9.8

t = (-8-11.08)/-9.8 = 1.947 s
or
t = (-8+11.08)/-9.8 = -0.31444 s
The second choice is rejected because the diver cannot hit the water "before" diving. However, the number is useful because its absolute value it represents the time the diver spent below the level of 3 m.

The diver spent a total of 1.947 seconds in the air, from the diving board to the water. Of this, 0.314 second was spent below the height of the board, leaving 1.633 above.

If we ignore air resistance (makes sense at theses slow speeds) it takes exactly the same time to go from 3 m to maximum height than it takes to fall from maximum height back to the level of the board.

Therefore, the diver goes upwards for half of 1.633 seconds.
The diver goes upwards for 0.8165 seconds (approx. 5/6 of a second) and reaches maximum height. The diver falls for 0.8165 second back to the level of the board plus another 0.314 second from the height of the board to the water.

upward = 0.8165
downward = 1.1305

Answer 2

If you do not understand your homework you should go see a tutor or get extra help after school, it is better that way you can actually learn why it is what it is.

Answer 3

3metre
.28 sec
up gravity