Consider a series of steps as shown. A ball is thrown from 0. Find the minimum speed to directly jump to 5th step
The Correct option is (C): \(5(\sqrt{(\sqrt2+1))} m/s\)
\(y=x\tan\theta-\frac{gx^2}{2v^2\cos^2\theta}\)
(2.5,2.5) must lie on this
\(⇒1=\tan\theta-\frac{g\times2.5}{2v^2\cos^2\theta}\)
\(⇒ \frac{25}{2v^2\cos^2\theta}=\tan\theta-1\)
\(⇒ v^2=\frac{25}{2}\left\{\frac{1+\tan^2\theta}{\tan\theta-1}\right\}\)
\(⇒ v_{min}=5\sqrt{\sqrt2+1}\)
[ Happens when \(\tan\theta=\sqrt2+1\) ]
The velocity (v) - time (t) plot of the motion of a body is shown below :
The acceleration (a) - time(t) graph that best suits this motion is :
A wheel of a bullock cart is rolling on a level road, as shown in the figure below. If its linear speed is v in the direction shown, which one of the following options is correct (P and Q are any highest and lowest points on the wheel, respectively) ?
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is:
The rate at which an object covers a certain distance is commonly known as speed.
The rate at which an object changes position in a certain direction is called velocity.
Read More: Difference Between Speed and Velocity