The angle of projection of a particle is measured from the vertical and is denoted by φ. If the projection speed is fixed and the maximum height reached is hₘ, which graph correctly represents hₘ as a function of φ?
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Question

The angle of projection of a particle is measured from the vertical and is denoted by φ. If the projection speed is fixed and the maximum height reached is hₘ, which graph correctly represents hₘ as a function of φ?

Options

G1 Physics · Accepted Answer

If φ is measured from the vertical, the initial vertical component of velocity is u y u_y u y ​ = u cosφ. Maximum height is hₘ = u y 2 / ( 2 g ) u_y²/(2g) u y 2 ​ / ( 2 g ) = u²cos²φ/(2g). At φ=0°, cosφ=1, so hₘ is maximum. At φ=90°, cosφ=0, so hₘ=0. Thus hₘ decreases continuously from its maximum value at φ=0° to zero at φ=90°. This corresponds to Graph 2. Correct option: B.