Answer to Question #103774 in Classical Mechanics for Josephine

Question

1. You've made it to the top deck on the diving tower, 10 m above both the ground level deck and the water, and 3 m wide. Your friend has dared you to run and jump horizontally, so as to go as far forwards as you can before hitting the water. But you see that the far side of the pool is only 10 m from the edge of your platform.

a) Treating yourself as a projectile (something only recommended in theory) travelling horizontally as you leave the platform. How fast would you have to run in order to travel 10 metres horizontally before hitting the water? Give your answer to only one significant figure.

b) What horizontal acceleration do you need to achieve the speed calculated in (a)?

3. Here, I am swinging a ball around in a horizontal circle with a radius of 0.60.
a) What is its vertical component of acceleration?
b) At what constant speed must it travel so that the horizontal component of its acceleration is 2.1 m/ s^2.

Answer 1

1) a)

$$x=vt$$

$$t=\sqrt{\frac{2h}{g}}$$ $$x=v\sqrt{\frac{2h}{g}}\to 10=v\sqrt{\frac{2(10)}{9.8}}$$

$$v=7\frac{m}{s}$$

b)

$$v^2=2a_xs\to 7^2=2(3)a_x$$

$$a_x=8.2\frac{m}{s^2}$$

3) a)

$$a_y=g=9.8\frac{m}{s^2}$$

b)

$$a_x=\frac{v^2}{r}$$

$$2.1=\frac{v^2}{0.6}$$

$$v=1.1\frac{m}{s}$$