A ball is thrown vertically upward. After t seconds, it reaches a certain height before falling back to the ground. This article delves into the physics behind this motion, examining the trajectory, velocity, and acceleration of the ball at different stages of its journey.

We will explore the factors influencing the ball’s maximum height and time of flight, providing a comprehensive understanding of the principles governing vertical motion.

Motion of a Vertically Thrown Ball: A Ball Is Thrown Vertically Upward. After T Seconds

When a ball is thrown vertically upward, it experiences an upward initial velocity and an initial height. The ball’s motion follows a parabolic trajectory due to the constant acceleration due to gravity acting downward.

Initial Conditions

The initial conditions of the ball’s motion are:

• Initial velocity (upward): v _i
• Initial height: h _i

Motion of the Ball

The ball’s motion is influenced by the acceleration due to gravity (g), which is approximately -9.8 m/s ²downward. The velocity and displacement of the ball at any time t can be calculated using the following equations:

• Velocity: v = v _i– gt
• Displacement: h = h _i+ v _it – 0.5gt ²

Maximum Height

The maximum height (h _max) reached by the ball occurs when its velocity becomes zero. This happens at a time t _maxgiven by:

t_max= v _i/g

The maximum height is then calculated as:

h_max= h _i+ 0.5v _i²/g

Time of Flight, A ball is thrown vertically upward. after t seconds

The total time of flight (t _f) of the ball is the time it takes to reach its maximum height and then return to the ground.

t_f= 2v _i/g

Impact on the Ground

Just before hitting the ground, the ball’s velocity is equal to its initial velocity but in the downward direction:

v_f=

v_i

The impact of the ball on the ground is an inelastic collision, meaning that the ball loses all its kinetic energy.

Helpful Answers

What is the maximum height reached by the ball?

The maximum height reached by the ball depends on its initial velocity and the acceleration due to gravity.

How long does it take for the ball to reach its maximum height?

The time it takes for the ball to reach its maximum height is equal to half of its total time of flight.

What is the velocity of the ball just before it hits the ground?

Just before hitting the ground, the ball’s velocity is equal in magnitude but opposite in direction to its initial velocity.