Ball Dropped from Accelerating Car – Rankers Physics
Topic: Kinematics
Subtopic: Equations of Motion

Ball Dropped from Accelerating Car

A car starts from rest and accelerates at \(5\text{ m/s}^2\). At \(t = 4\text{ s}\), a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at \(t = 6\text{ s}\)? (Take \(g = 10\text{ m/s}^2\))
\(20\sqrt{2} m/s, 10 m/s^2\)
\(20 m/s, 5 m/s^2\)
\(20 m/s, 0\)
\(20\sqrt{2} m/s, 0\)

Solution:

At \(t = 4\text{ s}\), the horizontal velocity is \(v_x = u + at = 0 + 5 \times 4 = 20\text{ m/s}\) and remains constant. In the vertical direction, the ball accelerates due to gravity for \(2\text{ s}\) (from \(t = 4\text{ s}\) to \(6\text{ s}\)), so \(v_y = gt = 10 \times 2 = 20\text{ m/s}\). The final velocity is \(v = \sqrt{v_x^2 + v_y^2} = 20\sqrt{2}\text{ m/s}\), and the acceleration is only due to gravity (\(10\text{ m/s}^2\)).

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