Question

For a given velocity, a projectile has the same range R for two angles of projection, if $t_{1}and{t}_2$ are the times of flight in the two cases then

• A. $t_1{t}_2\propto R^2$
• B. $t_1{t}_2\propto R$
• C. $t_1{t}_2\propto \frac{1}{R^2}$
• D. $t_1{t}_2\propto \frac{1}{R}$

Answer 1

The correct option is B

$t_1{t}_2\propto R$

As we know for complementary angles will have the same range for a projectile with a given velocity.
Therefore,
$t_1=\frac{2u\times sin{\theta }_1}{g}$
$t_2=\frac{2u\times sin{\theta }_2}{g}$
$sin{\theta }_1+sin{\theta }_2={90}^o$
$t_1{t}_2=\frac{2R}{g}\therefore t_1{t}_2\propto R$
Where,
$R=\frac{(u{)}^2\times sin2\theta }{g}$