Question

A ball of mass M is thrown vertically upwards. Another ball of mass 2M is thrown at an angle $\theta$ with the vertical. Both of them stay in air for the same period of time. The heights attained by the two are in the ratio.

• A. 1: 2
• B. 2: 1
• C. 1: 1
• D. $1:cos\theta$

Answer 1

Answer: (D)

$1:cos\theta$

Time of flight in case (1) $=$ case (2)

$\frac{2V_1}{g}=\frac{2V_2\sin \theta }{g}\Rightarrow V_1=V_2\sin \theta$

max height reacted by $\left(1\right)=\frac{V_1^2}{2g}=H_1$

max height reacted by $\left(2\right)=\frac{{\left(V_{2}sin\theta \right)}^2}{2g}=H_2$

$\Rightarrow H_1=H_2$.