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Part A: Football kicked at 45 degrees with an initial velocity of 25 m/s
Given:
Initial velocity (magnitude): 25 m/s
Launch angle: 45 degrees
Acceleration due to gravity: 9.8 m/s²
Time of flight:
Time of flight = 2 * (initial vertical velocity) / acceleration due to gravity
Initial vertical velocity = initial velocity * sin(angle)
Initial vertical velocity = 25 m/s * sin(45 degrees) = 17.68 m/s
Time of flight = 2 * (17.68 m/s) / 9.8 m/s² ≈ 3.62 seconds
Horizontal distance:
Horizontal distance = initial velocity * cos(angle) * time of flight
Horizontal distance = 25 m/s * cos(45 degrees) * 3.62 s ≈ 63.64 meters
Peak height:
Peak height = (initial vertical velocity)^2 / (2 * acceleration due to gravity)
Peak height = (17.68 m/s)^2 / (2 * 9.8 m/s²) ≈ 16.01 meters
Therefore, for Part A, the football has a time of flight of approximately 3.62 seconds, a horizontal distance of approximately 63.64 meters, and a peak height of approximately 16.01 meters.
Now let's move on to Part B.
Part B: Long jumper with an initial velocity of 12 m/s at an angle of 28 degrees above the horizontal
Given:
Initial velocity (magnitude): 12 m/s
Launch angle: 28 degrees
Acceleration due to gravity: 9.8 m/s²
Time of flight:
Time of flight = 2 * (initial vertical velocity) / acceleration due to gravity
Initial vertical velocity = initial velocity * sin(angle)
Initial vertical velocity = 12 m/s * sin(28 degrees) ≈ 5.53 m/s
Time of flight = 2 * (5.53 m/s) / 9.8 m/s² ≈ 1.13 seconds
Horizontal distance:
Horizontal distance = initial velocity * cos(angle) * time of flight
Horizontal distance = 12 m/s * cos(28 degrees) * 1.13 s ≈ 10.36 meters
Therefore, for Part B, the long jumper has a time of flight of approximately 1.13 seconds and a horizontal distance of approximately 10.36 meters. The peak height was not requested in Part B of the problem.
Please note that these calculations are approximations and may vary slightly depending on the precision of the calculations used.re with others. Click here ...
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