Question

Two balls are thrown from an inclined plane at angle of projection $\alpha$ with the plane one up the incline plane and other down the incline as shown in the figure. If $R_1$ & $R_2$ be their respective ranges and $h_1$ & $h_2$ be their respective maximum height then
[here $T_1$ & $T_2$ are times of flight in the two cases respectively]

• A. $h_1=h_2$
• B. $R_2-R_1=T_1^2$
• C. $R_2-R_1=\text{g sin}\theta T_2^2$
• D. $R_2-R_1=\text{g sin}\theta T_1^2$

Answer 1

Answer: (A), (C), (D)

$R_2-R_1=\text{g sin}\theta T_1^2$

$R_1=\frac{2u^{2}sin\alpha cos(\alpha +\theta )}{gco{s}^2\theta }$
and $h_1=\frac{u^{2}si{n}^2\alpha }{2gcos\beta }$
$R_2=\frac{2u^{2}sin\alpha cos(\alpha -\theta )}{gco{s}^2\theta }$
and $h_2=\frac{u^{2}si{n}^2\alpha }{2gcos\beta }$
hence $h_1=h_2$
$R_2-R_1=\text{g sin}\theta T_2^2$
$R_2-R_1=\text{g sin}\theta T_1^2$