s man travel on train and throw a ball straight up relative to the train with speed of 4.90m/s the train has a velocity of 20.0m/sdue east so what is the ball's total time of flight?
To find the ball's total time of flight, we need to consider the horizontal and vertical components separately.
First, let's calculate the time it takes for the ball to reach its maximum height (when it momentarily stops before falling back down). Since there is no horizontal acceleration, the ball's horizontal velocity is unaffected by its vertical motion. Therefore, the time taken to reach the maximum height can be calculated using the vertical component only.
Given:
Initial vertical velocity (upward) of the ball, V₀y = 4.90 m/s
Vertical acceleration, a = -9.8 m/s² (due to gravity)
Using the formula of motion in the vertical direction:
Vf = V₀y + at
We know that when the ball reaches its maximum height, its final vertical velocity (Vf) would be zero. So we can rearrange the formula to solve for time (t):
0 = V₀y + at
Simplifying the equation, we get:
t = -V₀y / a
Substituting the given values, we can calculate the time taken to reach the maximum height.
t = -4.90 m/s / -9.8 m/s²
t = 0.5 seconds
Now, to find the total time of flight, we need to consider both the time taken to reach the maximum height and the time taken for the ball to fall back down. Since the ball follows a parabolic trajectory, the total time of flight is twice the time taken to reach the maximum height.
Total time of flight = 2 * t_max_height
Total time of flight = 2 * 0.5 seconds
Total time of flight = 1 second
Therefore, the ball's total time of flight is 1 second.