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 \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32
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