Show that for a projectile the angle between the velocity and the x-axis as a function of time is given by
`theta(t) = tan^(-1) [(v_(oy)-g t)/(v_(o x))]`

What is the relation between angular velocity omega , frequenct v and time period T?

In figure shows that (v_x, t), and (v_y,t) for a body unit mass. Find the force as a function of tiime.

Shows that the projection angle theta_o for a projectile launched from the origin is given by theta_o=tan^-1((4h_m)/R) where the symbols have their usual meaning.

If x = g(t) and y = f(t) , find (d^2y)/(dx^2) as a function of t.

A curve is represented parametrically by the equations x = e^t cos t and y = e^t sin t where t is a parameter. Then The relation between the parameter 't' and the angle a between the tangent to the given curve andthe x-axis is given by, 't' equals

The time of flight of a body projected with initial velocity u at an angle theta is T. What will be th time of flight if thebody is projected with same velocity at an angle (90^@- theta) ?

Time taken of decay for a nuclear reaction is given by t=4t_(1//2) . The relation between the mean life (T) and time of decay (t) is given by : a) 2 T In 2 b) 4 T In 2 c) 2 T^(4) In 2 d) (1)/(T^(2)) In 2

A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity.From the plot shown in the figure. indicate the one that represents the velocity (v) of the pebble as a function of time (t).

Show that the equation of the line through the origin and making an angle theta with the line y = mx+c is : y/x= (m +- tan theta)/(1 overset(-)(+) m tan theta) .

Differentiate the following functions w.r.t x using first principle. f(x) = tan x