Answer to Question #225044 in Mechanics | Relativity for nina

Question

A child runs straight off the end of a diving platform at a (horizontal) speed of ⃗v0. The platform is H=10.0 m above the surface of the water and the child lands a horizontal distance of D=1.43 m.

A. Calculate the time required for the child to reach the water.

B. Calculate v0.

C. Calculate the magnitude of the child’s velocity when they hit the water.

D. Calculate the direction of the velocity when the child hits the water

Answer 1

The child move in two directions: horizontal and vertical. Let x-axis directed towards child's move before he jumped, and y-axis directed down. Then child moving can be write:

$\begin{cases} x=x_0+v_{0x}t\\ y=y_0+v_{0y}t+gt^2/2\\ v_0=v_{0x} \end{cases}$

$\begin{cases} D=v_{0x}t\\ H=gt^2/2\\ v_0=v_{0x} \end{cases}$

$\begin{cases} D=v_{0}t\\ H=gt^2/2\\ \end{cases}$

$\begin{cases} v_0=D\sqrt\dfrac{g}{2H}=1.43\dfrac{1}{\sqrt{2}}\approx1\\ t=\sqrt\dfrac{g}{2H}\approx0.7\\ \end{cases}$

$v_x=v_{0x}=v_0=1\\ v_y=v_{0y}+gt=7=>v=\sqrt{1^2+7^2}\approx7.1$

$\tan{\alpha}=\dfrac{v_x}{v_y}\approx1.41$

Answers:

A. 0.7s

B. 1m/s

C. 7.1 m/s

D. $\tan{\alpha}\approx1.41$