Question

A swimmer bounces straight up from a diving board and falls feet first into a pool. She starts with a velocity of 4.00 m/s, and her takeoff point is 1.80 m above the pool. (a) How long are her feet in the air? (b) What is her highest point above the board? (c) What is her velocity when her feet hit the water?

Answer 1

The swimmer's feet are in the air for approximately 0.41 seconds. The highest point above the board is approximately 0.8 meters. The swimmer's velocity when her feet hit the water is approximately -1.02 m/s.

Step-by-step explanation:

To answer these questions, we need to consider the motion of the swimmer as she jumps from the diving board. Let's solve each part step by step:

(a) To find how long her feet are in the air, we can use the formula:

time = (final velocity - initial velocity) / acceleration

Since the swimmer's motion is only influenced by gravity, the acceleration will be -9.8 m/s² (negative due to the downward motion). Assuming she goes up and then down symmetrically, her final velocity at the highest point will be 0. Using these values, we can find the time:

time = (0 - 4) / -9.8

Calculating the expression gives us a time of approximately 0.41 seconds.

(b) The highest point above the board can be determined by finding the displacement at that point. Since the swimmer starts with an initial velocity of 4.0 m/s and reaches a final velocity of 0, we can use the formula:

displacement = (final velocity² - initial velocity²) / (2 * acceleration)

Substituting the values, we get:

displacement = (0² - 4²) / (2 * -9.8)

Simplifying the expression yields a displacement of approximately 0.8 meters above the board.

(c) The velocity when her feet hit the water can be found using the equation:

final velocity = initial velocity + (acceleration * time)

Since we know the initial velocity, acceleration, and time, we can substitute the values and calculate:

final velocity = 4 + (-9.8 * 0.41)

This results in a final velocity of approximately -1.02 m/s, which means her feet hit the water with a downward velocity of 1.02 m/s.

Answer 2

a) Her feet are in the air for 0.73+0.41 = 1.14 seconds

b) Her highest height above the board is 0.82 m

c) Her velocity when her feet hit the water is 7.16 m/s

Step-by-step explanation:

t = Time taken

u = Initial velocity = 4 m/s

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 9.81 m/s²

`v=u+at\\\Rightarrow 0=4-9.81* t\\\Rightarrow (-4)/(-9.81)=t\\\Rightarrow t=0.41\ s`

`s=ut+(1)/(2)at^2\\\Rightarrow s=4* 0.41+(1)/(2)* -9.81* 0.41^2\\\Rightarrow s=0.82\ m`

b) Her highest height above the board is 0.82 m

Total height she would fall is 0.82+1.8 = 2.62 m

`s=ut+(1)/(2)at^2\\\Rightarrow 2.62=0t+(1)/(2)* 9.81* t^2\\\Rightarrow t=\sqrt{(2.62* 2)/(9.81)}\\\Rightarrow t=0.73\ s`

a) Her feet are in the air for 0.73+0.41 = 1.14 seconds

`v=u+at\\\Rightarrow v=0+9.81* 0.73\\\Rightarrow v=7.16\ m/s`

c) Her velocity when her feet hit the water is 7.16 m/s