Final answer:
The time of flight for the ball thrown horizontally from a height of 1 m is approximately 0.45 seconds, and the initial horizontal velocity needed to land 5 m away is approximately 11.11 m/s. This assumes the only force affecting the vertical motion is gravity with an acceleration of 9.81 m/s^2.
Step-by-step explanation:
The question asks about the time of flight and initial velocity of a ball thrown horizontally from a given height. This scenario is an example of projectile motion, which is a common topic in high school physics. We can calculate the time of flight based on the vertical motion under gravity, as horizontal motion does not affect the time it takes for an object to fall a certain vertical distance. The initial horizontal velocity can then be calculated using the time of flight.
Time of Flight (a)
The time of flight is determined solely by the vertical distance the ball falls and the acceleration due to gravity (which is approximately 9.81 m/s2). From the equation of motion for constant acceleration (s = ut + 1/2 at2), we can find the time t:
s: vertical distance = 1 m
u: initial vertical velocity = 0 m/s (since the ball is thrown horizontally)
a: acceleration due to gravity = 9.81 m/s2
1 m = 0 x t + 1/2 x 9.81 m/s2 x t2
t2 = 2 x 1 m / 9.81 m/s2
t = √(2/9.81 m/s2)
The time of flight is approximately 0.45 seconds.
Initial Horizontal Velocity (b)
With the time of flight determined, we can now calculate the initial horizontal velocity (vx) using the horizontal distance (d) and time (t):
d = vx x t
5 m = vx x 0.45 s
vx = 5 m / 0.45 s
The initial horizontal velocity is approximately 11.11 m/s.