91Ó°ÊÓ

A stone is dropped into a well and the sound of splash is heard after 4 seconds. Assuming the velocity of sound to be \(350 \mathrm{~m} / \mathrm{s}\) find the depth of the well.

A motorist takes 10 seconds to cover a distance of \(20 \mathrm{~m}\) and 15 seconds to cover a distance of \(40 \mathrm{~m} .\) Find the uniform acceleration of the car and the velocity at the end of 15 seconds. \(\left[0.267 \mathrm{~m} / \mathrm{s}^{2}, 4.7 \mathrm{~m} / \mathrm{s}\right]\)

Water drips at the rate of 5 drops per second from a leaking tap. Determine the vertical distanhe between two consecutive drops after the lower drop has attained a velocity of \(3 \mathrm{~m} / \mathrm{s}\). [Hint: First dro

A lift moves up with a constant acceleration upto a height of \(900 \mathrm{~m}\) and \(300 \mathrm{~m}\) with constant retardation and then comes to rest. Determine : \((\alpha)\) aceeleration, \((b)\) retardation and (c) the maximum velocity of the lift if the total time of travel is 30 seconds and the acceleration is one third of the retardation. \(\quad\left[3.55 \mathrm{~m} / \mathrm{s}^{2}, 10.65 \mathrm{~m} / \mathrm{s}^{2}, 80 \mathrm{~m} / \mathrm{s}\right]\)

A particle starts with an initial velocity of \(8 \mathrm{~m} / \mathrm{s}\) and moves along a straight line. It's acceleration time \(t\) after start is given by the expression \(A-B t\) where \(A\) and \(B\) are constants. stops. Hint: \(\left[\begin{array}{ll}t=0, & v=8 \mathrm{~m} / \mathrm{s} \\\ t=0 & x=0 \\ t=5 s & x=40 \\ t=5 s & v=0\end{array}\right] \quad\left[x=8 t+1.6 t^{2}-0.32 t^{3}\right]\)

A particle falls vertically in a medium whose resistance is proportional to the velocity of the particle. Find the velocity and distance travelled by the particle after a time \(t\). Hint: \(\left(\begin{array}{l}\text { Resistance, } R=k v^{2} \\ m a=m g-k v^{2}\end{array}\right) \quad\left(\begin{array}{l}v=\frac{g}{k}\left(1-e^{-k t}\right) \\ x=\left(\frac{g}{k} t+\frac{g}{k^{2}} e^{-k t}-\frac{g}{k^{2}}\right)\end{array}\right)\)