If a tank holds 5000 gallons of water, which drains from the bttomof the tank in 40 minutes, then torricelli's Law gives the volume Vof water remaining in the tank after t minutes ${\displaystyle (1-{\frac{t}{40}}^2)5000=V0\le t\le 40}$.
Find the rate at which water is draining from the tank after (a) 5min, (b) 10 min. At what time is the water flowing out the fastest?the slowest?

A block of mass m=2.20 kg slides down a 30 degree incline which is 3.60 m high. At the bottom, it strikes a block of mass=7.00 kg which is at rest on a horizontal surface in the picture. If the collision is elastic, and friction can be ignored, determine (a)the speeds of the two blocks after the collision, and (b) how far back up the incline the smaller mass will go.

A block is on a frictionless table, on earth. The block accelerates at ${\displaystyle 5.3\frac{m}{s^2}}$ when a 10 N horizontal force is applied to it. The block and table are set up on the moon. The acceleration due to gravity at the surface of the moon is ${\displaystyle 1.62\frac{m}{s^2}}$. A horizontal force of 5N is applied to the block when it is on the moon. The acceleration imparted to the block is closest to: 
a) ${\displaystyle 2.9\frac{m}{s^2}}$ 
b) ${\displaystyle 3.2\frac{m}{s^2}}$ 
c) ${\displaystyle 3.4\frac{m}{s^2}}$ 
d) ${\displaystyle 2.7\frac{m}{s^2}}$ 
e) ${\displaystyle 2.4\frac{m}{s^2}}$

If the coefficient of static friction between your coffeecup and the horizontal dashboard of your car is, how fast can you drive on a horizontal roadwayaround a right turn radius of 30.0 m before the cup starts toslide? If you go too fast, in what direction will the cupslide relative to the dashboard?

Two adults and a child want to push a wheeled cart in thedirection marked x in Fig. 4.29 The two adults push with horizontalforces ${\displaystyle F_1\text{and}{F}_2}$ as shown in the figure. (a)Find the magnitude and direction of the smallest force that thechild should exerts the minimum force found in part (a), the cartaccelerates at 2.0 ${\displaystyle \frac{m}{s^2}}$ in the +x direction. What is theweight of the cart?