Projectile Motion

Projectile motion refers to the motion of an object that is projected into the air and then follows a curved path due to the influence of gravity. The trajectory of the object is determined by its initial velocity and launch angle. In this case, a ball is projected with a velocity of 20 meters per second at an angle of 30 degrees with the horizontal.

Time of Flight

The time of flight is the total time it takes for the ball to complete its trajectory and return to the same horizontal level from which it was launched. To calculate the time of flight, we need to consider the vertical motion of the ball.

Vertical Motion

The vertical motion of the ball can be analyzed independently of the horizontal motion because they are independent of each other. The only force acting on the ball in the vertical direction is gravity, which causes it to accelerate downwards.

Initial Vertical Velocity

The initial vertical velocity of the ball can be calculated using trigonometry. As the ball is projected at an angle of 30 degrees with the horizontal, we can use the sine function to find the vertical component of the initial velocity.

Vertical component of initial velocity (Vy) = Velocity * sin(angle)
= 20 * sin(30)
= 10 meters per second

Time of Ascent

The time of ascent is the time it takes for the ball to reach its highest point in the trajectory. At this point, the vertical velocity becomes zero before the ball starts descending.

The time of ascent can be determined using the equation of motion:

Final vertical velocity (Vf) = Initial vertical velocity (Vi) + Acceleration (a) * Time (t)

As the final vertical velocity is zero at the highest point, we can rearrange the equation to solve for time:

0 = 10 - 9.8 * t

Simplifying the equation, we find:

t = 10 / 9.8
t ≈ 1.02 seconds

Total Time of Flight

Since the ball takes the same amount of time to ascend and descend, the total time of flight is twice the time of ascent.

Total time of flight = 2 * time of ascent
= 2 * 1.02
= 2.04 seconds

Therefore, the time of flight for the ball projected with a velocity of 20 meters per second at an angle of 30 degrees with the horizontal is approximately 2.04 seconds.

2 second