Question

Two objects A and B are thrown upward simultaneously with the same speed. The mass of A is greater than that of B. Suppose the air exerts a constant and equal force of resistance on the two bodies.
(a) The two bodies will reach the same height.
(b) A will go higher than B.

(c) B will go higher than A.
(d) Any of the above three may happen depending on the speed with which the objects are thrown.

Answer 1

(b) A will go higher than B.

Let the air exert a constant resistance force = F (in downward direction).
Acceleration of particle A in downward direction due to air resistance, a_A = F/m_A.
Acceleration of particle B in downward direction due to air resistance, a_B = F/m_B.
m_A > m_B
a_A < a_B
$S=ut+\frac{1}{2}a{t}^2$
$\mathrm{So},H_A=ut-\frac{1}{2}(a_A+g)t^2$
$H_B=ut-\frac{1}{2}(a_B+g)t^2$
$H_A>H_B$

Therefore, A will go higher than B.