The initial value problem

$\rm \frac{dy}{dt}+2y=0, y(0)=1$

is solved numerically using the forward Euler’s method with a constant and positive time step of Δt. 

Let 𝑦_𝑛 represent the numerical solution obtained after 𝑛 steps. The condition |𝑦_n+1| ≤ |𝑦_n| is satisfied if and only if Δt does not exceed _____________.

(Answer in integer)

The options show frames consisting of rigid bars connected by pin joints. Which one of the frames is non-rigid? 

A spherical ball weighing 2 kg is dropped from a height of 4.9 m onto an immovable rigid block as shown in the figure. If the collision is perfectly elastic, what is the momentum vector of the ball (in kg m/s) just after impact?

Take the acceleration due to gravity to be 𝑔 = 9.8 m/s². Options have been rounded off to one decimal place.

Air (density = 1.2 kg/m³, kinematic viscosity = 1.5 × 10^-5 m²/s) flows over a flat plate with a free-stream velocity of 2 m/s. The wall shear stress at a location 15 mm from the leading edge is τ_w. What is the wall shear stress at a location 30 mm from the leading edge?