# An object is thrown horizontally from a height how does the time of flight and the range of the object change when the magnitude of initial velocity tripled?

Mar 17, 2018

When an object is thrown horizontally from constant height $h$ with a velocity $u$,if it takes time $t$ to reach the ground,considering vertical motion only,we can say,

$h = \frac{1}{2} g {t}^{2}$ (using, $h = u t + \frac{1}{2} g {t}^{2}$ ,here$u = 0$ as initially no component of velocity was present vertically)

so,$t = \sqrt{\frac{2 h}{g}}$

So,we can see this expression is independent of initial velocity $u$,so on tripling $u$ there will be no effect on time of flight.

now,if it went upto $R$ horizontally in this time,then we can say,its range of motion, $R = u t = \sqrt{\frac{2 h}{g}} u$ (as,$u$ remains constant through out)

So,we can see,from the above expression that, $R \propto u$

So,on tripling $u$ range will also get tripled.