The runner had an initial vertical velocity of -0.7 m/s and an initial horizontal velocity of 3.6 m/s. If the forces were applied over a period of 0.2 seconds, what are the runner's final vertical and horizontal velocities?
Physics · High School · Thu Feb 04 2021
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To determine the final velocities of the runner, we need to know the forces applied in both the vertical and horizontal directions during the 0.2 seconds. However, based on the information provided, it appears that we do not have the values or directions of the forces that were applied to the runner. Without this information, we cannot calculate the change in velocity (acceleration) using Newton's second law (Force = mass x acceleration), and therefore we cannot determine the final velocities.
If no additional forces are applied (other than gravity, which affects vertical motion), the horizontal velocity of the runner will remain constant because there is no horizontal force mentioned, provided air resistance is negligible. The horizontal velocity would remain at 3.6 m/s.
For vertical motion, gravity would be the only force acting on the runner if no other vertical forces are mentioned. However, we would expect the vertical velocity to change due to gravity, which causes an acceleration of approximately -9.81 m/s² (downward). We also see there's an initial vertical velocity of -0.7 m/s, which indicates the runner is moving downwards. If the runner is in free fall and no other forces are acting in the vertical axis (ignoring air resistance), we can calculate the final vertical velocity after 0.2 seconds due to gravity.
The formula to calculate the final velocity (v_f) is: v_f = v_i + a * t
where: v_i = initial velocity (-0.7 m/s) a = acceleration due to gravity (-9.81 m/s²) t = time (0.2 seconds)
Using this formula: v_f = -0.7 m/s + (-9.81 m/s² * 0.2 seconds) v_f = -0.7 m/s - 1.962 m/s v_f = -2.662 m/s
So, the final vertical velocity of the runner would be -2.662 m/s if only the force of gravity were acting on the runner over 0.2 seconds. This velocity is negative because it's directed downwards.
Remember, to get a comprehensive answer, we need the external forces applied during the 0.2 seconds, and these calculations assume the absence of other vertical forces apart from gravity.