Question

Q: The cannons in the diagram below are being fired horizontally off platforms of the different heights(as indicated). While each cannon shoots an identical cannonball, they do so with differentvelocities. Given the height of the platform and each cannon's launch velocity, what is the correctranking, from greatest to least, for the range achieved by each cannonball?

Please show your work

Answer 1

Answer:

B: D > A = C > B

Explanation:

Time of flight (t) = $\sqrt{\frac{2h}{g} }$   (H = Height, G (Gravity) = 9.8m/s²)

Range = Velocity × Time = v$\sqrt{\frac{2h}{g} }$

Range of A = 1000 × $\sqrt{\frac{4-9x2}{9-8} }$= 1000m

Range of B = 500 × $\sqrt{\frac{9 x8x2}{9x8} }$= 707.1m

Range of C = 500 × $\sqrt{\frac{19x6x2}{9x8} }$= 1000m

Range of D = 750 x $\sqrt{\frac{19x6x2}{9x8} }$= 1500m

So, Order is: D > A = C > B (Option B)