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A projectile is fired with a speed u at ...

A projectile is fired with a speed `u` at an angle `theta` with the horizontal. Find its speed when its direcrtion of motion makes an angle `alpha` with the horizontal.

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To solve the problem of finding the speed of a projectile when its direction of motion makes an angle \( \alpha \) with the horizontal, we can follow these steps: ### Step 1: Understand the Components of Motion In projectile motion, the motion can be analyzed in two dimensions: horizontal (x-direction) and vertical (y-direction). The initial velocity \( u \) can be broken down into its components: - Horizontal component: \( u_x = u \cos \theta \) - Vertical component: \( u_y = u \sin \theta \) ### Step 2: Analyze the Horizontal Motion ...
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Knowledge Check

  • A projectile is projected with a speed u at an angle theta with the horizontal. What is the speed when its direction of motion makes an angle theta//2 with the horizontal

    A
    `(u cos theta)/(2)`
    B
    `u cos theta`
    C
    `u (2 cos (theta)/(2) - sec (theta)/(2))`
    D
    `u (cos(theta)/(2) - sec(theta)/(2))`

  • A particle is projected with a speed u at an angle theta with the horizontal. What will be the speed of the particle when direction of motion of particle is at an angle alpha with the horizontal?

    A
    `u cos theta sec alpha`
    B
    `u sec theta cos alpha`
    C
    `u cos theta tan alpha`
    D
    `u cos theta cot alpha`

  • A projectile is fired with a velocity u at an angle theta with the ground. At some instant during motin, its velocity makes an angle alpha with the horizontal direction. The speed of the particle at this time will be

    A
    `u cos theta sec alpha`
    B
    `u cos theta cos alpha`
    C
    `u^(2)cos^(2) alpha sin^(2)alpha`
    D
    `u sin theta sin alpha`

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    Assertion A particle is projected with speed u at an angle theta with the horizontal. At any time during motion, speed of particle is v at angle alpha with the vertical, then v sin alpha is always constant throughout the motion. Reason In case of projectile motion, magnitude of radical acceleration at topmost point is maximum.

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