an arrow is shot into the air with an initial velocity of 100m is at elevation of 60 degree find.
a the time of flight
b the maximum height attained
c the range
True
a 17.32 sec
b 374.95 or 375m
c 866m
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To find the time of flight, maximum height attained, and range of an arrow shot into the air, given an initial velocity of 100 m/s and an elevation angle of 60 degrees, we can use the principles of projectile motion.
a) Time of Flight:
The time of flight is the total time the arrow is in the air before it lands. We can use the formula for time of flight in projectile motion:
Time of flight = 2 * (Vertical component of initial velocity) / (acceleration due to gravity)
Since the arrow is shot at an angle of 60 degrees, we need to find the vertical component of the initial velocity. We can use trigonometry to find this:
Vertical component of initial velocity = Initial velocity * sin(elevation angle)
Plugging in the values we have:
Vertical component of initial velocity = 100 m/s * sin(60 degrees) = 100 * √3/2 = 50√3 m/s
Using this value, we can now calculate the time of flight:
Time of flight = 2 * (50√3 m/s) / (9.8 m/s²) ≈ 10.207 seconds
b) Maximum Height Attained:
To find the maximum height attained by the arrow, we can use the formula:
Maximum height = (Vertical component of initial velocity)² / (2 * acceleration due to gravity)
Plugging in the values we already have:
Maximum height = (50√3 m/s)² / (2 * 9.8 m/s²) ≈ 637.76 meters
c) Range:
To find the range, which is the horizontal distance covered by the arrow, we can use the formula:
Range = (Horizontal component of initial velocity) * Time of flight
To find the horizontal component of initial velocity, we can again use trigonometry:
Horizontal component of initial velocity = Initial velocity * cos(elevation angle)
Plugging in the values we have:
Horizontal component of initial velocity = 100 m/s * cos(60 degrees) = 100 * 1/2 = 50 m/s
Finally, we can calculate the range:
Range = (50 m/s) * (10.207 seconds) ≈ 510.35 meters
Therefore:
a) The time of flight is approximately 10.207 seconds.
b) The maximum height attained is approximately 637.76 meters.
c) The range is approximately 510.35 meters.