A parachutist, whose weight (actually mass) is 64 kg, drops from a helicopter 5000 m. above the ground. She falls towards the earth under the influence of gravity. Assume that the gravitational force is constant. Assume that the force due to air resistance is proportional to the velocity of the parachutist. The proportionality constant is sec when the parachute is closed, and is sec
when it is open. If the parachute does not open until 1 minute after the parachutist leaves the helicopter, after how many seconds will she hit the ground?
A point estimate of the mean length of life of the motors is given by the sample mean (\(\bar{x}\)), which is calculated as: \[ \bar{x} = \frac{\sum x_i}{n} \] where: - \(x_i\) are the individual ________ ________ ________ ____ ____ _______ __________ _____.
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When an aeroplane ascends from take-off to an altitude of 10 km, by how much does the gravitational attraction acting on it decrease?
A string of length l is connected to a fixed point at one end and to a stick of mass m at the other. The stick is whirling in a circle at constant velocity v . Use dimensional analysis to find the equation of the force in the string.
A particle of mass m moves on a straight line towards the centre of attraction, starting from rest at a distance a from the centre. Its velocity at a distance x from the centre varies as . Find the law of force.
A parachutist, whose weight (actually mass) is 64 kg, drops from a helicopter 5000 m. above the ground. She falls towards the earth under the influence of gravity. Assume that the gravitational force is constant. Assume that the force due to air resistance is proportional to the velocity of the parachutist. The proportionality constant is sec when the parachute is closed, and is sec
when it is open. If the parachute does not open until 1 minute after the parachutist leaves the helicopter, after how many seconds will she hit the ground?
A particle moving in .H.S M has got the velocities cm8 /sec and cm6 /sec when it is at distance cm3 and cm4 respectively from the centre of its motion. Determine the period and the amplitude of motion.
Consider the epidemic model governed by the following equation
with initial condition x = n at t = 0 . Here )t(x is the number of susceptibles at time ,t β is the contact rate. The population is assumed to be closed and homogeneously mixing. Let the contact rate be 0.002 and the number of susceptibles be 5000 initially
i) Find the density of the population when the rate of appearance of new cases is maximum.
ii) Find the time (in weeks) at which the rate of appearance of new cases is maximum.
iii) Obtain the maximum rate of appearance of new cases.
Consider the following system of equations
Find the nature of the critical point ,0( of the corresponding linear system.