Question

A projectile is thrown with a speed of 10√2 m/s at an angle of 45⁰ with the horizontal. The Time interval between the moments when its speed is √125m/s is (g = 10m/s²)

• A. 1.0 s
• B. 0.6 s
• C. 1.2 s
• D. 0.8

Answer 1

The correct option is A

1.0 s

Let $\varphi$ is the angle which the projectile's velocity is making with the horizontal at the moment when its speed is $\sqrt{125}\frac{m}{s}$. from the fact that horizontal component of
velocity of projectile is constant, we have -

$U\cos \theta =v\cos \theta \varphi$
$\Rightarrow 10\sqrt{2}\times \frac{1}{\sqrt{2}}=\sqrt{125}\cos \varphi$

$\Rightarrow \cos \varphi =\frac{2}{\sqrt{5}}$

Required time,
$t=\frac{2v\sin \varphi }{g}=1sec$.