A basketball player throws a chall -1 kg up with an initial speed of his hand at shoulder height = 2.15 m Le gravitational potential energy

Question

A basketball player throws a chall -1 kg up with an initial speed of his hand at shoulder height = 2.15 m Le gravitational potential energy ber ground level the ball leves 50% .(a) Give the total mechanical energy of the ball E in terms of maximum height Am it reaches, the mass m, and the gravitational acceleration g.(b) What is the height, hm in meters?

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Edana Edana 3 years 2021-09-04T16:08:20+00:00 1 Answers 0 views 0

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  1. thienan
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    2021-09-04T16:09:58+00:00
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    Complete Question:

    A basketball player tosses a basketball m=1kg straight up with an initial speed of v=7.5 m/s. He releases the ball at shoulder height h= 2.15m. Let gravitational potential energy be zero at ground level

    a)  Give the total mechanical energy of the ball E in terms of maximum height hn it reaches, the mass m, and the gravitational acceleration g.

    b) What is the height, hn in meters?

    Answer:

    a) Energy = mghₙ

    b) Height, hₙ = 5.02 m

    Explanation:

    a) Total energy in terms of maximum height

    Let maximum height be hₙ

    At maximum height, velocity, V=0

    Total mechanical energy , E = mgh + 1/2 mV^2

    Since V=0 at maximum height, the total energy in terms of maximum height becomes

    Energy = mghₙ

    b) Height,  hₙ in meters

    mghₙ = mgh + 1/2 mV^2

    mghₙ = m(gh + 1/2 V^2)

    Divide both sides by mg

    hₙ = h + 0.5 (V^2)/g

    h = 2.15m

    g = 9.8 m/s^2

    V = 7.5 m/s

    hₙ = 2.15 + 0.5(7.5^2)/9.8

    hₙ = 2.15 + 2.87

    hₙ = 5.02 m

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