A ball is thrown so that its initial vertical and horizontal components of velocity at 40 m/s and 20 m/s, respectively. Use a motion diagram to estimate the ball’s total time of flight and the distance it traverse before hitting the ground?
Answer please
To estimate the ball's total time of flight and the distance it traverses before hitting the ground, we can use the motion diagram and the principles of projectile motion.
Step 1: Analyze the motion horizontally
Since there is no horizontal acceleration, the horizontal motion is constant. As a result, the time of flight will be the same as the vertical motion. So, first, let's calculate the time of flight.
Time of flight (t) = Distance / Horizontal velocity
Given: Horizontal velocity (Vx) = 20 m/s
To calculate the distance, we need to know the time of flight and the horizontal velocity.
Distance (d) = Vx * t
Step 2: Analyze the motion vertically
The vertical motion of the ball involves acceleration due to gravity (g).
The vertical motion can be divided into two parts:
1. Upward motion: The ball starts at an initial vertical velocity (Vy) of 40 m/s and moves upward against gravity. The ball reaches its maximum height and then starts to fall down.
2. Downward motion: The ball starts to fall down with an initial vertical velocity of 0 m/s.
To calculate the time taken during the upward motion, we use the equation:
t = (Vy - Vf) / g
where:
Vy = initial vertical velocity = 40 m/s
Vf = final vertical velocity (at the topmost point) = 0 m/s
g = acceleration due to gravity ≈ 9.8 m/s²
Using this equation, we can calculate the time taken during the upward motion.
Step 3: Calculate the time of flight
The total time of flight is the sum of the upward and downward motion times.
Total time of flight (T) = 2 * (time taken during upward motion)
Step 4: Calculate the distance
The distance traveled horizontally can be calculated using the time of flight and the horizontal velocity.
Distance (d) = Horizontal velocity (Vx) * Total time of flight (T)
By following these steps, you can estimate the ball's total time of flight and the distance it traverses before hitting the ground.