derive expression for horizontal range
Hi Khadija, as one throws a body with a velocity u at an angle @ then the horizontal component u cos @ will not change as there is no acceleration in the horizontal direction
So u cos @ always remains constant
Now as we get the time of flight then we can easily get the horizontal range just by multiplying u cos @ by that time of flight
To get time of flight we have to use the formula s = ut + 1/2 * a * t^2
S = 0 (total displacement +h - h = 0)
u = u sin @ (vertical component)
a = - g
t = time of flight T
Plug and we get 0 = u isn @ T - 1/2 * g * T^2
Or T = 2 u sin @ / g
So we can get the expression for Range R = u cos @ * 2 u sin @ / g
Recalling 2 sin A cos A = sin 2A
we can write R = u^2 sin 2@ / g
So u cos @ always remains constant
Now as we get the time of flight then we can easily get the horizontal range just by multiplying u cos @ by that time of flight
To get time of flight we have to use the formula s = ut + 1/2 * a * t^2
S = 0 (total displacement +h - h = 0)
u = u sin @ (vertical component)
a = - g
t = time of flight T
Plug and we get 0 = u isn @ T - 1/2 * g * T^2
Or T = 2 u sin @ / g
So we can get the expression for Range R = u cos @ * 2 u sin @ / g
Recalling 2 sin A cos A = sin 2A
we can write R = u^2 sin 2@ / g