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Questions >> TN XII Math >> Differential Calculus Applications - I

At noon, ship $A$ is $100$ km west of ship $B$ . Ship $A$ is sailing east at $35$ km/hr and ship $B$ is sailing north at $25$ km/hr. How fast is the distance between the ships changing at $4.00$ pm.

asked May 1, 2013 by poojasapani_1

1 answer

The altitude of a triangle is increasing at a rate of $1\; cm/min$ while the area of the triangle is increasing at a rate of $2 \;cm^{2}/min$ . At what rate is the base of the triangle changing when the altitude is $10$ cm and the area is $100\;cm^{2}$

asked May 1, 2013 by poojasapani_1

1 answer

Newton's law of cooling is given by $\theta=\theta_0^{\circ}e^{-kt},$ where the excess of temperature at zero time is $0^{\circ}_{\circ}C$ and at time $t$ seconds is $\theta ^{\circ}C$ . Determine the rate of change of temperature after $40 s,$ given that $\theta_{\cdot}=16^{\circ}C$ and $k=-0.03.\qquad (e^{1.2}=3.3201)$

asked Apr 30, 2013 by poojasapani_1

1 answer

The distince $x$ meters traveled by a vehical in time $t$ seconds after the brakes are applied is given by: $\;x=20 t-\large\frac{5}{3}$ $t^{2}$ . Determine the distance the car travelled before it stops.

asked Apr 30, 2013 by poojasapani_1

1 answer

The distince $x$ meters traveled by a vehical in time $t$ seconds after the brakes are applied is given by: $\;x=20 t-\large\frac{5}{3}$ $t^{2}$ . Determine the speed of the vehicle (in km/hr) at the instant the brakes are applied

asked Apr 30, 2013 by poojasapani_1

1 answer

A particle of unit mass moves so that displacement after $t$ secs is given by $x=3\cos(2t-4).$ Find the acceleration and kinetic energy at the end of $2 \;secs.[ K.E =\large\frac{1}{2}$ $mv^{2}\quad m$ is mass]

asked Apr 30, 2013 by poojasapani_1

1 answer

A missile fired from ground level rises $x$ metres vertically upwards in $t$ seconds and $x=100t-\large\frac{25}{2}t^{2}$ find the velocity with which the missile strikes the ground

asked Apr 30, 2013 by poojasapani_1

1 answer

A missile fired from ground level rises $x$ metres vertically upwards in $t$ seconds and $x=100t-\large\frac{25}{2}t^{2}$ find the maximum hight reached .

asked Apr 30, 2013 by poojasapani_1

1 answer

A missile fired from ground level rises $x$ metres vertically upwards in $t$ seconds and $x=100t-\large\frac{25}{2}t^{2}$ find the time when the height of the missile is a maximum

asked Apr 30, 2013 by poojasapani_1

1 answer

A missile fired from ground level rises $x$ metres vertically upwards in $t$ seconds and $x=100t-\large\frac{25}{2}t^{2}$ find the initial velocity of the missile.

asked Apr 30, 2013 by poojasapani_1

1 answer

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