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A ball is thrown vertically upward with an initial speed of 20m/s. Two second later a stone is thrown vertically (from the same initial height as the ball) with an intial speed of 24m/s . At what height above the release point will the ball and stone pass each other?
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A ball is thrown vertically upward with an initial speed of 20m/s. Two...
Problem Statement:

A ball is thrown vertically upward with an initial speed of 20m/s. Two second later a stone is thrown vertically (from the same initial height as the ball) with an intial speed of 24m/s . At what height above the release point will the ball and stone pass each other? Explain in details.


Solution:


  • Let's first calculate the maximum height reached by the ball.

  • Using the equation of motion, v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration (which is -9.8m/s^2 for upward motion), and s is the displacement (maximum height reached).

  • At the highest point, the final velocity is zero. So, 0 = 20^2 - 2*9.8*s

  • Solving for s, we get s = 20.41m

  • Now, let's find the time taken by the ball to reach this height.

  • Using the equation of motion, s = ut + 0.5at^2, where t is the time taken.

  • Substituting the values, 20.41 = 20*t + 0.5*(-9.8)*t^2

  • Solving for t, we get t = 2.09s

  • Now, let's find the height reached by the stone after 2 seconds.

  • Using the same equation of motion, s = ut + 0.5at^2, where u = 24m/s and t = 2s.

  • Substituting the values, s = 24*2 + 0.5*(-9.8)*2^2

  • Solving for s, we get s = 19.2m

  • Now, we know that the ball and stone will pass each other at some height between 19.2m and 20.41m.

  • Let's assume that they pass each other at a height of x meters above the release point.

  • The time taken by the ball to reach this height would be 2.09 - (x/20) seconds (since the ball takes 2.09 seconds to reach 20.41m and travels x meters less).

  • The time taken by the stone to reach this height would be 2 - (x/24) seconds (since the stone takes 2 seconds to reach 19.2m and travels x meters less).

  • Since they pass each other at this height, the time
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A ball is thrown vertically upward with an initial speed of 20m/s. Two second later a stone is thrown vertically (from the same initial height as the ball) with an intial speed of 24m/s . At what height above the release point will the ball and stone pass each other?
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A ball is thrown vertically upward with an initial speed of 20m/s. Two second later a stone is thrown vertically (from the same initial height as the ball) with an intial speed of 24m/s . At what height above the release point will the ball and stone pass each other? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A ball is thrown vertically upward with an initial speed of 20m/s. Two second later a stone is thrown vertically (from the same initial height as the ball) with an intial speed of 24m/s . At what height above the release point will the ball and stone pass each other? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball is thrown vertically upward with an initial speed of 20m/s. Two second later a stone is thrown vertically (from the same initial height as the ball) with an intial speed of 24m/s . At what height above the release point will the ball and stone pass each other?.
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