Question

a shell fired from a cannon at 60 ° from horizontal strikes a target 20m high at a distance 80m. Calculate the initial velocity

Answer 1

consider the motion along the X-direction

X = horizontal displacement = 80 m

$V_{ox}$ = initial velocity along the x-direction = v Cos60

t = time of travel

using the equation

X = $V_{ox}$   t

80 = (v Cos60) (t)

t = 160/v                                         eq-1

consider the motion in vertical direction :

Y = vertical displacement = 20 m

$V_{oy}$  = initial velocity in Y-direction = v Sin60

a = acceleration = - 9.8 m/s²

t = time of travel = 160/v

using the equation

Y = $V_{oy}$  t + (0.5) a t²

20 = (v Sin60) (160/v) + (0.5) (- 9.8) (160/v)²

v = 32.5 m/s