- #1

Benjamin_harsh

- 211

- 5

- Homework Statement
- Is my formulae correct for time of flight in this projectile problem?

- Relevant Equations
- Is my formulae correct for time of flight in this projectile problem?

##V_{oy} = V_{0}.sinθ = (20 m/sec)(sin 30) = 10 m/sec##

##V_{ox} = V_{0}.cosθ = (20 m/sec)(cos 30) = 17.3 m/sec##

##y = y_{0} + V_{oy}t - \large\frac {1}{2}\normalsize gt^{2}##

##0 = 50 + 10t - 4.9t^{2}##

##0 = 4.9t/6{2} - 10t - 50##

##t = \large\frac {-b±\sqrt {b^{2} - 4ac}}{2a}##

##t = \large\frac {10 ±\sqrt {100 - 4(4.9)(-50)}}{9.8}##

##t = \large\frac {10 ± 32.86}{9.8}\normalsize = 4.37 sec \;(or) -2.33 sec##

##Y_{max}##; Max height = ##\large\frac {V^{2}sin^{2}θ}{2g} + \normalsize H = \large\frac {100}{19.6} \normalsize + H = 55.102m ##

**My formulae**= I simple add these two time intervals 1) Time it takes from A to travel to B;

##T_{A → B} = \large\frac{V_{0}.sinθ}{g}##

##= \large\frac{10}{9.8} \normalsize = 1.0204 sec.##

2) Time it takes for for B to travel to C; ##T_{B→C} =\large\sqrt\frac {2.y_{max}}{g}##

##= \large\sqrt\frac {2.(55.102)}{9.8}\normalsize = 3.353 sec####T_{A → B} + T_{B→C} = 4.37 sec##

Is my formulae correct for time of flight in this projectile problem?