A car starts from rest and accelerates at 5 m/s². At t = 4 s, a ball is dropped out of a window by a

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Question

A car starts from rest and accelerates at 5 m/s². At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What are the velocity and acceleration of the ball at t = 6 s? (Take g = 10 m/s²)

Accepted Answer

Correct Answer: A — 20√2 m/s, 10 m/s²Step-by-step Solution:At t = 4 s, velocity of car = u + at = 0 + 5 × 4 = 20 m/s (horizontal). At the moment of release, the ball has the same horizontal velocity as the car: vx = 20 m/s. Once released, no horizontal force acts (ignoring air resistance), so vx remains 20 m/s.Time after release = 6 - 4 = 2 s. Vertical velocity acquired: vy = g × t = 10 × 2 = 20 m/s.Resultant velocity at t = 6 s: v = √(vx² + vy²) = √(20² + 20²) = √800 = 20√2 m/s.After release, the only force on the ball is gravity, so acceleration = g = 10 m/s² (downward).Why other options are incorrect: Option B incorrectly gives the acceleration as 5 m/s² (the car's acceleration no longer acts on the ball after release). Options C and D state acceleration = 0, which is incorrect since gravity acts on the ball throughout.Key Concept: Once the ball is released from the moving car, it undergoes projectile motion. It retains the horizontal velocity of the car at the instant of release and accelerates vertically under gravity. The car's acceleration no longer applies to the ball.

A car starts from rest and accelerates at 5 m/s². At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What are the velocity and acceleration of the ball at t = 6 s? (Take g = 10 m/s²)

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A car starts from rest and accelerates at 5 m/s². At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What are the velocity and acceleration of the ball at t = 6 s? (Take g = 10 m/s²)

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