Ask Question
21 February, 06:10

A ball is thrown eastward into the air from the origin (in the direction of the positive x-axis). The initial velocity is 60 i + 64 k, with speed measured in feet per second. The spin of the ball results in a southward acceleration of 6 ft/s2, so the acceleration vector is a = - 6 j - 32 k. Where does the ball land? (Round your answers to one decimal place.) ft from the origin at an angle of ° from the eastern direction toward the south. With what speed does the ball hit the ground? (Round your answer to one decimal place.)

+1
Answers (1)
  1. 21 February, 09:39
    0
    The ball's position in the air at time t is given by the vector,

    p (t) = (60 i + 64 k) t + 1/2 (-6 j - 32 k) t ²

    and its velocity is given by

    v (t) = (60 i + 64 k) + (-6 j - 32 k) t

    The ball is in the air for as long as it takes for the vertical (k) component of the position vector to reach 0, so we solve,

    64 t - 32/2 t ² = 0 = => t = 0 OR t = 4

    and so the ball is in the air for 4 s.

    After this time, the ball has position vector

    p (4) = (60 i + 64 k) t + 1/2 (-6 j - 32 k) t ² = 240 i - 48 j

    which has magnitude

    ||p (4) || = √ (240² + (-48) ²) = 48 √26 ≈ 244.8 ft

    in a direction θ in the x, y plane from the positive x axis such that

    tanθ = - 48/240 = - 1/5 = => θ = - arctan (1/5) ≈ - 11.3º

    or 11.3º South of East.

    The ball hits the ground with speed

    ||v (4) || = ||60 i - 24 j - 64 k|| = √ (60² + (-24) ² + (-64) ²) = 4 √517 ≈ 91.0 ft/s
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A ball is thrown eastward into the air from the origin (in the direction of the positive x-axis). The initial velocity is 60 i + 64 k, with ...” in 📙 Physics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers