Question

Is time ascent depends on mass of projected body

Answer 1

No, time of ascent of a body does not depend on its mass

The time of ascent in projectile motion is given by,

T = 2vsin

$t = 2v \sin( \alpha ) \div g$

where alpha is the angle of ascent

Answer 2

Does time of ascent depend upon the mass of projected body?

• No, it doesn't depend on the mass of the object.

Let mass be m , initial velocity of vertical projection be u and the time taken to reach the topmost point be t :

Applying 1st Equation of Kinematics:

$\therefore \: v = u + at$

$\implies \: 0 = u + ( - g)t$

$\implies \: 0 = u - gt$

$\implies \: gt = u$

$\implies \: t= \dfrac{u}{g}$

$\implies \: t \propto {m}^{0}$

[Hence proved].

• This is true even for a 2D projectile motion.

• After calculations, the time of ascent comes as:

$\therefore \: t = \dfrac{u \sin( \theta) }{g}$

$\implies \: t \propto {m}^{0}$

[Hence Verified here as well]