The angle of projection for which maximum height is equal to the range covered will be? a)76 deg. b)tan-4. c)both

1 Answer
Mar 5, 2018

Arctan 4 = 76 degrees

Explanation:

The explanation involves using the position equation for both horizontal and vertical directions, evaluating height and range and setting them equal.
The position equation is
s(t) = s0+v0t+12at2
which for horizontal and vertical directions reduces to
sv(t)=v0sinxt12gt2
sh(t)=v0cosxt

solving for time of flight (tof) which is when sv(t)=0
0=t(v0 sinx - g t / 2) ........ tof = 2 v0sinxg

Range = sh ( tof) = v0cosx(2v0sinxg)
Range = sh ( tof) = 2v20cosx(sinxg)
Height = sv( tof/2 ) = v0sinx(v0sinxg)g2(v0sinxg)2
Height = (v0sinx)22g
Set these 2 expressions equal to get
(v0sinx)22g=2v20cosxsinxg
which simplifies to .....
sinx /2 = 2 cosx
tan x = 4
x = arctan 4 = 75.9 degrees