Q2.7-46 PE - College Physics (Urone)

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 take-off point is   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?

Step-by-Step Solution

Answer

(a)  1.14 s

(b)  0.82 m 

(c) 7.16 m/s 

Free falling body

The above case is of the free-falling body. In case of the free falling body the acceleration is considered as the gravitational acceleration.

If the body is moving upward, it is considered negative, if the body is moving downward g is considered positive.

The initial velocity of the swimmer is 4 m/s 

Time taken by the swimmer in air

Time taken = t  

Initial velocity = u= 4 m/s 

Final velocity = v = 0 

Acceleration when going upwards = -9.8 m/s²

$$\begin{gathered} v=u+gt \\ 0=4+\left(-9.81\right)\left(t\right) \\ t=0.41 s \end{gathered}$$ 

Hence the time taken by the swimmer in air half- way is 0.41s. 

a) The highest height above the board is h m, can be calculated by the equation of motion

 $$\begin{gathered} h=ut+\frac{1}{2}g{t}^2 \\ h=\left(4\right)\left(0.41\right)+\frac{1}{2}\left(-9.81\right){\left(0.41\right)}^2 \\ h=0.82 m \end{gathered}$$

Hence the highest point above the board is 0.82 meter.

The total height covered by her will be

 $$\begin{gathered} h=0.82+1.8 \\ =2.62 m \end{gathered}$$

Time taken by the swimmer in air

Hence the total time she spends in air will be

 $$\begin{gathered} h=ut+\frac{1}{2}g{t}^2 \\ 2.62=\left(0\right)\left(t\right)+\frac{1}{2}\left(9.81\right){\left(t\right)}^2 \\ t=\sqrt{\frac{2.62\times 2}{9.81}} \\ t=0.73 s \end{gathered}$$

Hence the time taken by the swimmer in air 

$$\begin{gathered} =0.73+0.41 \\ =1.14 s \end{gathered}$$ 

The time taken by the swimmer in air is 1.14s.

Velocity when her feet hits water

Velocity can be calculated by putting the value in equation

  $$\begin{gathered} v=u+gt \\ V=0+\left(9.81\right)\left(0.73\right) \\ V=7.16 m/s \end{gathered}$$

Velocity when her feet hit the water is 7.16 m/s.

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.