Answer to Question #206458 in Physics for Morgan Hopkin

Question

The entire physics class does not submit their physics labs and Miss Takken is really angry! And when Miss Takken gets angry she gets even. So Miss Takken locks the class in a cage and walks 350 m away with her cannon. She fires a cannonball at an angle of 34° above the horizontal and with a velocity of 60.0 m/s. (Not based on a true story!)

a.         Is the class toast or safe?

b.     Mr. Lacey gets in on the act and tells Miss Takken that she can adjust the cannon to another angle to hit the class. What angle does Mr. Lacey tell her to adjust it to?     

c.     Describe two other methods that Miss Takken might employ to nail the class besides adjusting the angle.

Answer 1

(a) Let's find the range of the cannonball:

$$R=\dfrac{v_0^2sin2\theta}{g},$$ $$R=\dfrac{(60\ \dfrac{m}{s})^2\cdot sin2\cdot34^{\circ}}{9.8\ \dfrac{m}{s^2}}=340.6\ m.$$

Since $340.6\ m < 350\ m$ the class will safe.

(b) We can find the angle as follows:

$$sin2\theta=\dfrac{Rg}{v_0^2},$$ $$2\theta=sin^{-1}(\dfrac{Rg}{v_0^2}),$$ $$2\theta=sin^{-1}(\dfrac{350\ m\cdot9.8\ \dfrac{m}{s^2}}{(60\ \dfrac{m}{s})^2})=72.32^{\circ},$$ $$\theta=\dfrac{72.32^{\circ}}{2}=36.16^{\circ}.$$

(c) She might adjust the velocity of the cannonball or decrease the distance to the cage.