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Show that for a projectile the angle bet...

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)((u_y-"gt")/(u_x))`

Answer

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Show that for a projectile the angle between the velocity and the X-axis as a function of the time Is given by theta(t) = tan^-1((v_(0y)-gt)/v_(alphax))

Show that the projection angle theta_0 for a projectile launched from the origin is given by theta_0=tan^(-1)((4H)/R) Where the symbols have their usual meaning.

Knowledge Check

  • Let the function g,(-oo,oo)rarr(-pi/2,pi/2) be given by g(u)=2tan^(-1)(e^u)-pi/2, Then ,g is

    A
    even and is strictly increasing in `(0,oo)`
    B
    odd and is strictly decreasing in `(-oo,oo)`
    C
    odd and is strictly increasing in `(-oo,oo)`
    D
    neither even nör ödd , but is strictly Increasing in `(-oo.oo)`

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    If x = a sec theta and y = b tan theta , then find the relation between x and y free from theta .

    Two straight lines u=0a n dv=0 pass through the origin and the angle between them is tan^(-1)(7/9) . If the ratio of the slope of v=0 and u=0 is 9/2 , then their equations are

    Show that the equation of the normal to the hyperbola x= a sec theta, y=b tan theta at the point ( a sec theta, b tan theta) is, ax cos theta + b y cot theta=a^(2)+b^(2) .

    A body is projected vertically upwards with an initial velocity u_1 . Another is projected with initial velocity u_2 at an angle theta with the horizontal . If both of them reach the same height ,show that sin theta=(u_1)/(u_2) .

    Maximum height of a projectile is H an range of projection is R when the projectile is projected with the velocity u. Show that R^2 = 16H (u^2/(2g)-H) .

    If 2u = 5x is the relation between the variables x and u and geometric mean of x is 1, find the geometric mean of u.

    If theta is the angle between the lines given by the equation 6x^2+5x y-4y^2+7x+13 y-3=0 , then find the equation of the line passing through the point of intersection of these lines and making an angle theta with the positive x-axis.

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