Question

1. you push your coffee off the table at a velocity v in the horizontal direction. after a time t, it impacts the ground. how far away from your desk must the carpet be to not get stained by the coffee? 6. draw a depiction of the stacks of textbooks on your desk & a corresponding free body diagram. what would cause your desk to collapse? 7. why do you weight less on the moon than you do on the earth? 8. how do average speed and average velocity differ? when would they be the same? 9. how do displacement and distance differ? when would they be the same?

Explanation:

5.

Step1: Recall horizontal - motion formula

In horizontal direction, there is no acceleration ($a_x = 0$). The kinematic equation for horizontal displacement is $x=v_x t$. Since the initial horizontal velocity is $v$ and time of flight is $t$, the horizontal displacement gives the distance from the desk.
$x = vt$

A depiction of stacks of textbooks on a desk would show books piled on top of each other. A free - body diagram would have the force of gravity ($F_g$) acting downwards on the textbooks and the normal force ($N$) exerted by the desk on the textbooks acting upwards. The desk would collapse if the total weight of the textbooks (and other objects on it) exceeds the maximum load - bearing capacity of the desk. This is related to the strength of the materials the desk is made of and its structural integrity.

Weight is given by $W = mg$, where $m$ is mass and $g$ is the acceleration due to gravity. The acceleration due to gravity on the Moon ($g_{moon}\approx1.62m/s^2$) is much less than that on Earth ($g_{earth}\approx9.8m/s^2$). Since mass is constant, a lower $g$ value on the Moon results in a lower weight.

Answer:

$vt$

6.